Pub Date : 2026-02-03DOI: 10.1016/j.compstruc.2026.108124
Rohit Satish Patil, Zhilin Han, Sofia G. Mogilevskaya
{"title":"The isogeometric boundary element algorithm for solving the plane strain problem of an elastic matrix containing an open material surface of arbitrary shape","authors":"Rohit Satish Patil, Zhilin Han, Sofia G. Mogilevskaya","doi":"10.1016/j.compstruc.2026.108124","DOIUrl":"https://doi.org/10.1016/j.compstruc.2026.108124","url":null,"abstract":"","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"117 1","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01DOI: 10.1016/j.compstruc.2026.108113
Wenxiong Li , Jiayuan Huang , Suiyin Chen , Gengying Li , Jianhua Wen
Efficient structural reanalysis for high-rank modifications is of significant importance in engineering computations that involve repeated solution of equilibrium equations, such as structural optimization and nonlinear analysis. This paper proposes a novel reanalysis method based on separation and reconstruction operations for structures with large-scale modifications. The core idea is to replace the solution of the structural equations corresponding to large-scale modifications with a sequence of solutions for locally modified structures. Consequently, the displacement solution of the modified structure can be reconstructed by aggregating the solutions from these locally modified structures. In the implementation, the relationship between each locally modified structure and the large-scale modified structure is formally characterized using high-dimensional model representation, and the reanalysis of locally modified structures is performed through an efficient computational framework that incorporates system reduction and preconditioned iterative solvers. To mitigate the errors arising from the omission of higher-order terms, a correction mechanism is introduced to eliminate residual errors in the equilibrium equations, thereby ensuring the accuracy of displacement solutions. The efficacy and computational advantages of the proposed method are demonstrated through numerical experiments. The results confirm that the method exhibits superior performance in handling structural reanalysis problems involving both large-scale modifications and local modifications.
{"title":"Structural reanalysis method based on separation-reconstruction mode for structures with large-scale modifications","authors":"Wenxiong Li , Jiayuan Huang , Suiyin Chen , Gengying Li , Jianhua Wen","doi":"10.1016/j.compstruc.2026.108113","DOIUrl":"10.1016/j.compstruc.2026.108113","url":null,"abstract":"<div><div>Efficient structural reanalysis for high-rank modifications is of significant importance in engineering computations that involve repeated solution of equilibrium equations, such as structural optimization and nonlinear analysis. This paper proposes a novel reanalysis method based on separation and reconstruction operations for structures with large-scale modifications. The core idea is to replace the solution of the structural equations corresponding to large-scale modifications with a sequence of solutions for locally modified structures. Consequently, the displacement solution of the modified structure can be reconstructed by aggregating the solutions from these locally modified structures. In the implementation, the relationship between each locally modified structure and the large-scale modified structure is formally characterized using high-dimensional model representation, and the reanalysis of locally modified structures is performed through an efficient computational framework that incorporates system reduction and preconditioned iterative solvers. To mitigate the errors arising from the omission of higher-order terms, a correction mechanism is introduced to eliminate residual errors in the equilibrium equations, thereby ensuring the accuracy of displacement solutions. The efficacy and computational advantages of the proposed method are demonstrated through numerical experiments. The results confirm that the method exhibits superior performance in handling structural reanalysis problems involving both large-scale modifications and local modifications.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108113"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01DOI: 10.1016/j.compstruc.2026.108123
Mohamed Elsayed Nassar , Ali Kandil , Andrey Nasedkin
<div><div>Polarization is a key stage in the manufacture of piezoelectric materials/composites. In a dense piezoceramic material, it is usually uniform with the polarization vector directed along the polarization axis. However, in non-uniform piezoceramic materials, such as piezocomposites with pores or inclusions, the polarization field is non-uniform and can significantly affect the properties of the composite. The heterogeneity of the polarization field is especially pronounced in piezocomposites with conductive inclusions or in porous composites with metal particles deposited on the pore boundaries. This study explores how the polarization process affects the primary elastic, piezoelectric, and dielectric coefficients of two piezoelectric composites, PZT–Air and PZT–Thin Metal Layer–Air (PZT–TML–Air). It is worth noting that the metal phase in PZT–TML–Air is a very thin layer around the outside surface of each pore, therefore the electrical conductivity characteristics are the primary influence of this layer, and the elastic properties of the metal are not significant. Therefore, the PZT–TML–Air composite can be considered as a two-phase material. A numerical homogenization approach including finite element analysis, representative volume element (RVE), perfect contact between different phases, linear essential boundary conditions, and the Hill-Mendel’s principle was employed to calculate the equivalent properties. A new random RVE, applicable to diverse two-phase dispersed composites, and an algorithm for its quick creation were introduced. This RVE is a cubic piezoelectric matrix with randomly distributed spherical inclusions of various volumes. It has a fill factor of up to 50%. We used two simplified strategies for determining inhomogeneous properties for the piezoceramic matrix, which are associated with the orientations of element coordinate systems (ECS) with inhomogeneous polarization fields. The first method solely analyzes inhomogeneities caused by ECS rotations, whereas the second takes into consideration changes in material moduli magnitudes and ECS directions caused by the polarization field. The polarization vectors were determined by solving the corresponding dielectric problem using the finite element approach. To carry out the computations, a set of programs for the ANSYS Mechanical APDL package was created, allowing for the automation of all steps of modeling and determining equivalent moduli. Therefore, the following procedures were automated for the most complicated instance of the PZT–TML-Air composite with non-uniform polarization, accounting for the change in the moduli and orientations of the ECS: computation of the moduli of non-uniformly polarized piezoelectric ceramics; construction of the RVE with specified properties and the finite element mesh; definition of ECS and polarization vector for each finite element; solution of a set of boundary value problems for a non-uniform piezoelectric material with post-processo
极化是压电材料/复合材料制造的关键阶段。在致密的压电陶瓷材料中，它通常是均匀的，偏振矢量沿着偏振轴方向。然而，在非均匀的压电陶瓷材料中，如带有孔隙或夹杂的压电复合材料，极化场是不均匀的，可以显著影响复合材料的性能。极化场的非均质性在含有导电夹杂的压电复合材料或在孔隙边界沉积金属颗粒的多孔复合材料中表现得尤为明显。本研究探讨极化过程如何影响PZT-Air和PZT-Thin Metal Layer-Air （PZT-TML-Air）两种压电复合材料的初级弹性系数、压电系数和介电系数。值得注意的是，PZT-TML-Air中的金属相是围绕每个孔外表面的非常薄的一层，因此电导率特性是该层的主要影响因素，金属的弹性性能不显著。因此，PZT-TML-Air复合材料可以看作是一种两相材料。采用有限元分析、代表性体积单元（RVE）、相间完美接触、线性基本边界条件和Hill-Mendel原理等数值均匀化方法计算等效性质。介绍了一种适用于多种两相分散复合材料的随机RVE及其快速生成算法。该RVE是具有随机分布的不同体积球形夹杂的立方压电基体。它的填充系数高达50%。我们使用两种简化策略来确定压电陶瓷矩阵的非均匀性，这些非均匀性与具有非均匀极化场的单元坐标系（ECS）的取向有关。第一种方法只分析了ECS旋转引起的不均匀性，而第二种方法考虑了极化场引起的材料模量和ECS方向的变化。采用有限元法求解相应的介电问题，确定极化矢量。为了进行计算，为ANSYS Mechanical APDL软件包创建了一套程序，允许自动化建模和确定等效模量的所有步骤。因此，对于最复杂的具有非均匀极化的PZT-TML-Air复合材料实例，考虑到ECS模量和取向的变化，自动执行以下步骤：计算非均匀极化压电陶瓷的模量；构造具有特定属性的RVE及有限元网格；定义每个有限元的ECS和极化矢量；基于平均单元应力分量和电感应矢量的等效模量后处理方法求解非均匀压电材料边值问题并计算了各种压电模量和优值。当考虑均匀极化场时，采用分析Mori-Tanaka均质技术对结果进行验证。由于极化矢量的微尺度色散，导电相的存在极大地影响了PZT-TML-Air的有效压电性能。计算结果表明，考虑极化场的不均匀性对于精确建模PZT-TML-Air复合材料至关重要，特别是当极化模型考虑了极化矢量的大小和方向时。因此，与均匀极化模型相比，流体静力学参数的变化可增加1.5倍。结果还表明，横向压电常数d31和转导系数TC31=d312/ε33T均有显著改善。这意味着压电复合材料PZT-TML-Air可以有效地用于横向传感和驱动应用以及水听器应用。
{"title":"Microstructural characterization of PZT–thin metal layer–air and PZT–air composites employing a random representative volume element (RVE) and heterogeneous polarization models","authors":"Mohamed Elsayed Nassar , Ali Kandil , Andrey Nasedkin","doi":"10.1016/j.compstruc.2026.108123","DOIUrl":"10.1016/j.compstruc.2026.108123","url":null,"abstract":"<div><div>Polarization is a key stage in the manufacture of piezoelectric materials/composites. In a dense piezoceramic material, it is usually uniform with the polarization vector directed along the polarization axis. However, in non-uniform piezoceramic materials, such as piezocomposites with pores or inclusions, the polarization field is non-uniform and can significantly affect the properties of the composite. The heterogeneity of the polarization field is especially pronounced in piezocomposites with conductive inclusions or in porous composites with metal particles deposited on the pore boundaries. This study explores how the polarization process affects the primary elastic, piezoelectric, and dielectric coefficients of two piezoelectric composites, PZT–Air and PZT–Thin Metal Layer–Air (PZT–TML–Air). It is worth noting that the metal phase in PZT–TML–Air is a very thin layer around the outside surface of each pore, therefore the electrical conductivity characteristics are the primary influence of this layer, and the elastic properties of the metal are not significant. Therefore, the PZT–TML–Air composite can be considered as a two-phase material. A numerical homogenization approach including finite element analysis, representative volume element (RVE), perfect contact between different phases, linear essential boundary conditions, and the Hill-Mendel’s principle was employed to calculate the equivalent properties. A new random RVE, applicable to diverse two-phase dispersed composites, and an algorithm for its quick creation were introduced. This RVE is a cubic piezoelectric matrix with randomly distributed spherical inclusions of various volumes. It has a fill factor of up to 50%. We used two simplified strategies for determining inhomogeneous properties for the piezoceramic matrix, which are associated with the orientations of element coordinate systems (ECS) with inhomogeneous polarization fields. The first method solely analyzes inhomogeneities caused by ECS rotations, whereas the second takes into consideration changes in material moduli magnitudes and ECS directions caused by the polarization field. The polarization vectors were determined by solving the corresponding dielectric problem using the finite element approach. To carry out the computations, a set of programs for the ANSYS Mechanical APDL package was created, allowing for the automation of all steps of modeling and determining equivalent moduli. Therefore, the following procedures were automated for the most complicated instance of the PZT–TML-Air composite with non-uniform polarization, accounting for the change in the moduli and orientations of the ECS: computation of the moduli of non-uniformly polarized piezoelectric ceramics; construction of the RVE with specified properties and the finite element mesh; definition of ECS and polarization vector for each finite element; solution of a set of boundary value problems for a non-uniform piezoelectric material with post-processo","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108123"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01DOI: 10.1016/j.compstruc.2026.108119
Ziheng Huang , Ju Chen , Shixing Liu , Yongxin Guo
The geometrically exact beam problems are often solved based on total Lagrangian method and updated Lagrangian method. However, these methods are prone to singularities and poor convergence when dealing with large deformations. The relative configuration vector method is proposed to obtain a singularity-free solution of the static equilibrium equations even for models with large deformation. First, the kinematic description of geometrically exact beams based on Lie group SE(3) is presented, along with an SE(3)-interpolation for the beam elements. The advantages of SE(3)-interpolation, such as objectivity and shear-locking-free behavior are then discussed. Next, an interpolation scheme for the variation of the average convective strain is derived, which allows for the computation of strain operators and static equilibrium equations without introducing complex operators. Subsequently, a detailed comparison is made among the three computing methods in terms of singularities, equivalence conditions for multivariable substitution, and the tangent stiffness matrix. Theoretically, the relative configuration vector method can inherently avoid the logarithm map and thereby eliminates the associated singularities. Finally, numerical examples are taken to show that the proposed relative configuration vector method avoids singularities and enhances convergence behavior under large deformations compared with the total and updated Lagrangian methods.
{"title":"A relative configuration vector method for solving geometrically exact beam problems","authors":"Ziheng Huang , Ju Chen , Shixing Liu , Yongxin Guo","doi":"10.1016/j.compstruc.2026.108119","DOIUrl":"10.1016/j.compstruc.2026.108119","url":null,"abstract":"<div><div>The geometrically exact beam problems are often solved based on total Lagrangian method and updated Lagrangian method. However, these methods are prone to singularities and poor convergence when dealing with large deformations. The relative configuration vector method is proposed to obtain a singularity-free solution of the static equilibrium equations even for models with large deformation. First, the kinematic description of geometrically exact beams based on Lie group SE(3) is presented, along with an SE(3)-interpolation for the beam elements. The advantages of SE(3)-interpolation, such as objectivity and shear-locking-free behavior are then discussed. Next, an interpolation scheme for the variation of the average convective strain is derived, which allows for the computation of strain operators and static equilibrium equations without introducing complex operators. Subsequently, a detailed comparison is made among the three computing methods in terms of singularities, equivalence conditions for multivariable substitution, and the tangent stiffness matrix. Theoretically, the relative configuration vector method can inherently avoid the logarithm map and thereby eliminates the associated singularities. Finally, numerical examples are taken to show that the proposed relative configuration vector method avoids singularities and enhances convergence behavior under large deformations compared with the total and updated Lagrangian methods.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108119"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01DOI: 10.1016/j.compstruc.2026.108117
Ganesh S. Pawar , Amar K. Gaonkar , Salil S. Kulkarni
In structural mechanics, thermomechanical coupling is essential for assessing the performance and safety of engineering systems. Finite element analysis is commonly used to model such problems; however, its high computational cost, particularly in non-linear scenarios, limits efficiency. This study introduces a hybrid reduced order model framework to address thermoelastic problems where the thermal part exhibits non-linearity while the mechanical part remains linear. The proposed hybrid reduced order model approach integrates reduction of the mechanical part using a modal or a Krylov bases while maintaining the thermal field at full-scale dimensions. In addition, a complete reduction is performed, where reduction of the thermal part is achieved through a two-tier process: proper orthogonal decomposition for primary reduction, followed by hyper-reduction techniques such as the energy conserving sampling and weighting and the discrete empirical interpolation method. Four distinct reduced order models are developed by combining different reduction techniques for the reduction of mechanical and thermal parts. The methodology is validated using 2D thermoelastic problems, demonstrating both accuracy and computational efficiency. Using nondimensional equations, an additional study is carried out to assess the influence of coupling on the sizes of different reduction quantities. This work advances reduced order model strategies for fully coupled physics problems.
{"title":"Model order reduction for fully coupled thermoelastic problems with non-linear temperature field","authors":"Ganesh S. Pawar , Amar K. Gaonkar , Salil S. Kulkarni","doi":"10.1016/j.compstruc.2026.108117","DOIUrl":"10.1016/j.compstruc.2026.108117","url":null,"abstract":"<div><div>In structural mechanics, thermomechanical coupling is essential for assessing the performance and safety of engineering systems. Finite element analysis is commonly used to model such problems; however, its high computational cost, particularly in non-linear scenarios, limits efficiency. This study introduces a hybrid reduced order model framework to address thermoelastic problems where the thermal part exhibits non-linearity while the mechanical part remains linear. The proposed hybrid reduced order model approach integrates reduction of the mechanical part using a modal or a Krylov bases while maintaining the thermal field at full-scale dimensions. In addition, a complete reduction is performed, where reduction of the thermal part is achieved through a two-tier process: proper orthogonal decomposition for primary reduction, followed by hyper-reduction techniques such as the energy conserving sampling and weighting and the discrete empirical interpolation method. Four distinct reduced order models are developed by combining different reduction techniques for the reduction of mechanical and thermal parts. The methodology is validated using 2D thermoelastic problems, demonstrating both accuracy and computational efficiency. Using nondimensional equations, an additional study is carried out to assess the influence of coupling on the sizes of different reduction quantities. This work advances reduced order model strategies for fully coupled physics problems.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108117"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01DOI: 10.1016/j.compstruc.2026.108121
Yixuan Zhang , Oren Lavan , Christian Málaga-Chuquitaype
Clutched Inerter Dampers integrate inerters with one-way clutches and dampers, enabling the inerters to disengage from the host structure and dissipate energy, suppressing undesirable energy feedback and avoiding the direct alteration of the structural period, making clutched inerter dampers particularly attractive for vibration mitigation and energy harvesting applications. However, the nonlinearity and discontinuity introduced by clutch engagement-disengagement mechanisms pose significant challenges for their accurate numerical modelling and optimization-based design. Existing optimization approaches for such systems are predominantly based on simplified or linearised numerical models, or on exhaustive parameter scanning, which either fail to capture the true nonlinear behaviour or become impractical for realistic design spaces.
We present an adjoint-based, gradient-driven optimization framework for structures equipped with clutched inerter dampers in which the Mixed Lagrangian Formalism is employed as the time-integration scheme. Within the proposed framework, the nonlinear behaviour of clutched inerter dampers is fully captured, while computational efficiency and numerical robustness are achieved through the Mixed Lagrangian Formalism, which reduces the cost of individual response-history analyses and enhances stability in the presence of non-smooth dynamics. In addition, adjoint-based sensitivity analysis significantly decreases the number of simulations required during the optimization process. The framework enables efficient optimization of design parameters as demonstrated through a series of representative case studies. Our results show that, despite strong nonlinearity and discontinuous system responses, analytical gradients can be consistently derived, leading to substantial reductions in computational cost and improved optimization efficiency.
While the actual performance may be influenced by the characteristics of the design landscape and the choice of initial conditions, the proposed framework provides a robust and extensible basis for further methodological developments. It can be readily extended in future work to accommodate alternative optimization strategies or enhanced formulations.
{"title":"Efficient optimization of clutched inerter dampers using mixed Lagrangian formalism","authors":"Yixuan Zhang , Oren Lavan , Christian Málaga-Chuquitaype","doi":"10.1016/j.compstruc.2026.108121","DOIUrl":"10.1016/j.compstruc.2026.108121","url":null,"abstract":"<div><div>Clutched Inerter Dampers integrate inerters with one-way clutches and dampers, enabling the inerters to disengage from the host structure and dissipate energy, suppressing undesirable energy feedback and avoiding the direct alteration of the structural period, making clutched inerter dampers particularly attractive for vibration mitigation and energy harvesting applications. However, the nonlinearity and discontinuity introduced by clutch engagement-disengagement mechanisms pose significant challenges for their accurate numerical modelling and optimization-based design. Existing optimization approaches for such systems are predominantly based on simplified or linearised numerical models, or on exhaustive parameter scanning, which either fail to capture the true nonlinear behaviour or become impractical for realistic design spaces.</div><div>We present an adjoint-based, gradient-driven optimization framework for structures equipped with clutched inerter dampers in which the Mixed Lagrangian Formalism is employed as the time-integration scheme. Within the proposed framework, the nonlinear behaviour of clutched inerter dampers is fully captured, while computational efficiency and numerical robustness are achieved through the Mixed Lagrangian Formalism, which reduces the cost of individual response-history analyses and enhances stability in the presence of non-smooth dynamics. In addition, adjoint-based sensitivity analysis significantly decreases the number of simulations required during the optimization process. The framework enables efficient optimization of design parameters as demonstrated through a series of representative case studies. Our results show that, despite strong nonlinearity and discontinuous system responses, analytical gradients can be consistently derived, leading to substantial reductions in computational cost and improved optimization efficiency.</div><div>While the actual performance may be influenced by the characteristics of the design landscape and the choice of initial conditions, the proposed framework provides a robust and extensible basis for further methodological developments. It can be readily extended in future work to accommodate alternative optimization strategies or enhanced formulations.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108121"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01DOI: 10.1016/j.compstruc.2026.108122
Chenfei Cao , Jie Hu , Xiaodong Huang , Xing Chen , Wenkang Cao , Jiachun Li
The traditional single-material topology optimization struggle to achieve optimal objective performance of thermo-mechanical structures, as they fail to enable free selection and combination of multiple materials in multi-material systems. To address this challenge, this paper proposes an efficient multi-material floating projection topology optimization method for thermo-mechanical structures. By integrating a linear material interpolation model with thermal stress coefficients, the proposed approach simultaneously addresses the issues of design dependence on thermoelastic loads and material parasitism in low-density regions. Besides, the developed thermo-mechanical coupled optimization framework incorporates combined thermal and mechanical loads, employs a single mass constraint to minimize structural compliance, and eliminates the need for conventional multiple volume constraints. Some 2D and 3D benchmark numerical examples confirm that the proposed method eliminates the need for selecting complex optimization parameters, such as multi-material penalty factors, yielding smoother topological configurations with more compact structures and more rational thermo-mechanical transfer performance. Notably, the proposed approach enables adaptive retention or removal of multi-material topological phases in structures under a single mass constraint, outperforming those conventional designs with multiple volume constraints and single-material designs of equal mass. The presented results provide valuable insights into multi-physics topology optimization and the design of composite engineering structures.
{"title":"Multi-material floating projection topology optimization of thermo-mechanical structures using a linear material model","authors":"Chenfei Cao , Jie Hu , Xiaodong Huang , Xing Chen , Wenkang Cao , Jiachun Li","doi":"10.1016/j.compstruc.2026.108122","DOIUrl":"10.1016/j.compstruc.2026.108122","url":null,"abstract":"<div><div>The traditional single-material topology optimization struggle to achieve optimal objective performance of thermo-mechanical structures, as they fail to enable free selection and combination of multiple materials in multi-material systems. To address this challenge, this paper proposes an efficient multi-material floating projection topology optimization method for thermo-mechanical structures. By integrating a linear material interpolation model with thermal stress coefficients, the proposed approach simultaneously addresses the issues of design dependence on thermoelastic loads and material parasitism in low-density regions. Besides, the developed thermo-mechanical coupled optimization framework incorporates combined thermal and mechanical loads, employs a single mass constraint to minimize structural compliance, and eliminates the need for conventional multiple volume constraints. Some 2D and 3D benchmark numerical examples confirm that the proposed method eliminates the need for selecting complex optimization parameters, such as multi-material penalty factors, yielding smoother topological configurations with more compact structures and more rational thermo-mechanical transfer performance. Notably, the proposed approach enables adaptive retention or removal of multi-material topological phases in structures under a single mass constraint, outperforming those conventional designs with multiple volume constraints and single-material designs of equal mass. The presented results provide valuable insights into multi-physics topology optimization and the design of composite engineering structures.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108122"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studying chloride diffusion in concrete is essential for predicting structural durability and designing corrosion-resistant materials and structures. While analytical models and finite element methods can simulate diffusion, they typically require large and high-quality datasets and do not possess advantages in parameter identification. Physics-Informed Neural Network, which integrates Fick 2nd law with initial and boundary conditions, offer a promising alternative. It not only replicates diffusion behavior accurately but also enhances the fitting of experimental data via a data-driven loss term and enable inverse estimation of diffusion related parameters. This paper outlines three key advantages of using this new method for problem-solving about chloride diffusion in concrete: (1) robustness to noise and low data requirements for one-dimensional inverse estimation of diffusion coefficients; (2) strategy integrates data, physics, and engineering insights for parameter inversion.; and (3) extended physics-informed frameworks with weak constraints for cracked concrete. Overall, Physics-Informed Neural Network provides a robust numerical tool for efficient durability assessment and the design of corrosion-resistant and resilient concrete structures. For self-healing concrete, the proposed framework effectively estimates diffusion coefficient in healed crack and accurately predicts long-term diffusion behavior, contributing to the optimal design and evaluation of self-healing materials.
{"title":"Physics-Informed neural network based inversion and prediction of natural chloride diffusion in uncracked and cracked concrete systems","authors":"Zhewen Huang , Senlin Xie , Kasyapa Sriram Kompella , Estefanía Cuenca , Stefano Mariani , Liberato Ferrara","doi":"10.1016/j.compstruc.2026.108120","DOIUrl":"10.1016/j.compstruc.2026.108120","url":null,"abstract":"<div><div>Studying chloride diffusion in concrete is essential for predicting structural durability and designing corrosion-resistant materials and structures. While analytical models and finite element methods can simulate diffusion, they typically require large and high-quality datasets and do not possess advantages in parameter identification. Physics-Informed Neural Network, which integrates Fick 2nd law with initial and boundary conditions, offer a promising alternative. It not only replicates diffusion behavior accurately but also enhances the fitting of experimental data via a data-driven loss term and enable inverse estimation of diffusion related parameters. This paper outlines three key advantages of using this new method for problem-solving about chloride diffusion in concrete: (1) robustness to noise and low data requirements for one-dimensional inverse estimation of diffusion coefficients; (2) strategy integrates data, physics, and engineering insights for parameter inversion.; and (3) extended physics-informed frameworks with weak constraints for cracked concrete. Overall, Physics-Informed Neural Network provides a robust numerical tool for efficient durability assessment and the design of corrosion-resistant and resilient concrete structures. For self-healing concrete, the proposed framework effectively estimates diffusion coefficient in healed crack and accurately predicts long-term diffusion behavior, contributing to the optimal design and evaluation of self-healing materials.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108120"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01DOI: 10.1016/j.compstruc.2026.108116
G. Cera , J.G. Rots , A.T. Slobbe , F. Messali
An existing interface material model for quasi-brittle fracture, originally developed within the Discrete Element Method framework, is implemented and enhanced for use in implicit Finite Element analyses of unreinforced masonry structures. The model captures mixed-mode fracture in tension-shear and combines cohesion with Coulomb friction in compression-shear. To address convergence issues arising when loading–unloading takes place, due to a discontinuity in the traction–separation relation, a regularization of the frictional contribution is proposed. A new model parameter is introduced and a calibration procedure to ensure numerical robustness and objectivity is presented. Furthermore, the consistent tangent stiffness matrix is derived to improve convergence in full-scale simulations. The improved model is applied within a simplified micromodelling approach to simulate the in-plane cyclic response of 2D masonry structures, including a shear wall and a spandrel subjected to a combination of horizontal and vertical actions. The results demonstrate that the model accurately reproduces key aspects of masonry behaviour, including stiffness degradation, energy dissipation, and crack patterns, while maintaining robustness and efficiency in complex cyclic loading scenarios.
{"title":"Modelling interface damage in masonry structures under cyclic loading conditions with cohesive fracture and regularized friction","authors":"G. Cera , J.G. Rots , A.T. Slobbe , F. Messali","doi":"10.1016/j.compstruc.2026.108116","DOIUrl":"10.1016/j.compstruc.2026.108116","url":null,"abstract":"<div><div>An existing interface material model for quasi-brittle fracture, originally developed within the Discrete Element Method framework, is implemented and enhanced for use in implicit Finite Element analyses of unreinforced masonry structures. The model captures mixed-mode fracture in tension-shear and combines cohesion with Coulomb friction in compression-shear. To address convergence issues arising when loading–unloading takes place, due to a discontinuity in the traction–separation relation, a regularization of the frictional contribution is proposed. A new model parameter is introduced and a calibration procedure to ensure numerical robustness and objectivity is presented. Furthermore, the consistent tangent stiffness matrix is derived to improve convergence in full-scale simulations. The improved model is applied within a simplified micromodelling approach to simulate the in-plane cyclic response of 2D masonry structures, including a shear wall and a spandrel subjected to a combination of horizontal and vertical actions. The results demonstrate that the model accurately reproduces key aspects of masonry behaviour, including stiffness degradation, energy dissipation, and crack patterns, while maintaining robustness and efficiency in complex cyclic loading scenarios.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108116"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1016/j.compstruc.2026.108118
Xin Chen, Gabriele Milani, Yiwei Hua
This paper presents an efficient method for stochastic homogenized kinematic limit analysis of three quasi-periodic masonry bond patterns subjected to in-plane loading. The proposed methodology involves two key points. Firstly, simplified 2D rigid-plastic homogenization models for three bond patterns are proposed. The kinematic limit analysis problem, incorporating proposed homogenization models, is then formulated and solved by linear programming to obtain deterministic failure surfaces. Secondly, the block heights and lengths of representative element of volume are treated as random variables, and the probability density evolution method is employed to obtain the probability information (such as means and probability density functions) of failure surfaces. Three numerical examples are investigated. The results show that the proposed method can accurately derive the probabilistic information of failure surfaces and achieving a computational cost that is ten times lower than Monte Carlo simulation.
{"title":"Stochastic homogenized kinematic limit analysis for three quasi-periodic masonry bond patterns under in-plane loading via probability density evolution method","authors":"Xin Chen, Gabriele Milani, Yiwei Hua","doi":"10.1016/j.compstruc.2026.108118","DOIUrl":"10.1016/j.compstruc.2026.108118","url":null,"abstract":"<div><div>This paper presents an efficient method for stochastic homogenized kinematic limit analysis of three quasi-periodic masonry bond patterns subjected to in-plane loading. The proposed methodology involves two key points. Firstly, simplified 2D rigid-plastic homogenization models for three bond patterns are proposed. The kinematic limit analysis problem, incorporating proposed homogenization models, is then formulated and solved by linear programming to obtain deterministic failure surfaces. Secondly, the block heights and lengths of representative element of volume are treated as random variables, and the probability density evolution method is employed<!--> <!-->to obtain the probability information (such as means and probability density functions) of failure surfaces. Three numerical examples are investigated. The results show that the proposed method can accurately derive the probabilistic information of failure surfaces and achieving a computational cost that is ten times lower than Monte Carlo simulation.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108118"},"PeriodicalIF":4.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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