Pub Date : 2025-08-26DOI: 10.1016/j.finel.2025.104432
Yassir Wardi, Pisey Keo, Mohammed Hjiaj
In this paper, we present a novel 3D nonlinear formulation for two-layered composite beams that accounts for interlayer slip in both longitudinal and lateral directions. Warping effects are included in a simplified manner, assuming that the warping of each layer does not contribute to the stress resultants of each section, allowing the use of the classical St. Venant warping function to define the warping shape of each subsection. The second-order approximation of the Green–Lagrange strain tensor, combined with linear constitutive laws, is integrated into the principle of virtual work to derive the tangent stiffness matrix of the composite element and its corresponding internal force. To address membrane and slip locking issues, we propose a new averaging strain technique, complemented by quadratic interpolation functions for the axial displacement of the two layers. To account for large displacements and rotations, the co-rotational approach is adopted. The co-rotated local reference frame is constructed by connecting end nodes located at the shear center of the bottom layer of the composite beam. As a result, special treatments are employed to address eccentric forces applied to the top layer of the composite beam. Finally, the performance of the proposed formulation is evaluated using four representative examples.
{"title":"Efficient co-rotational formulation for 3D composite beams with two-directional interlayer slip","authors":"Yassir Wardi, Pisey Keo, Mohammed Hjiaj","doi":"10.1016/j.finel.2025.104432","DOIUrl":"10.1016/j.finel.2025.104432","url":null,"abstract":"<div><div>In this paper, we present a novel 3D nonlinear formulation for two-layered composite beams that accounts for interlayer slip in both longitudinal and lateral directions. Warping effects are included in a simplified manner, assuming that the warping of each layer does not contribute to the stress resultants of each section, allowing the use of the classical St. Venant warping function to define the warping shape of each subsection. The second-order approximation of the Green–Lagrange strain tensor, combined with linear constitutive laws, is integrated into the principle of virtual work to derive the tangent stiffness matrix of the composite element and its corresponding internal force. To address membrane and slip locking issues, we propose a new averaging strain technique, complemented by quadratic interpolation functions for the axial displacement of the two layers. To account for large displacements and rotations, the co-rotational approach is adopted. The co-rotated local reference frame is constructed by connecting end nodes located at the shear center of the bottom layer of the composite beam. As a result, special treatments are employed to address eccentric forces applied to the top layer of the composite beam. Finally, the performance of the proposed formulation is evaluated using four representative examples.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104432"},"PeriodicalIF":3.5,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-08-22DOI: 10.1016/j.finel.2025.104435
Matteo Sorrenti, Marco Gherlone
<div><div>This work presents some numerical and experimental validations of the free-vibration behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory (<span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span>). The <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> formulation enhances the Timoshenko's kinematics with a piece-wise zigzag cubic distribution of the axial displacement, and a smoothed parabolic variation for the transverse deflection. Simultaneously, an a-priori assumption is made for the transverse normal stress and the transverse shear one: the former is assumed to be a third-order power series expansion of the thickness coordinate, while the latter is derived through the integration of Cauchy's equations. The equations of motion and consistent boundary conditions for the free-vibration problem are derived through the Hellinger-Reissner (HR) theorem. Taking advantage of the C<sup>0</sup>-continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated, i.e., the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> element. The analytical and FE performances of the proposed <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> model are first addressed by means of a comparison with high-fidelity 3D FE models. Subsequently, an experimental campaign is conducted using LASER Doppler Vibrometry (LDV) to evaluate the modal parameters of a series of thick sandwich beams made of aluminium alloy face-sheets and Rohacell® WF110 core. The experimental results concerning the natural frequencies and modal shapes of the thick sandwich beam specimens under free-free boundary conditions are compared with those given by <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> and high-fidelity 3D FE models. The numerical-experimental assessment highlights the effect of core and face-sheet thickness on frequency estimations, as well as the complexity of reproducing in the numerical model the experimental uncertainties. In general, the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span
{"title":"An experimental and numerical dynamic study of thick sandwich beams using a mixed {3,2}-RZT formulation","authors":"Matteo Sorrenti, Marco Gherlone","doi":"10.1016/j.finel.2025.104435","DOIUrl":"10.1016/j.finel.2025.104435","url":null,"abstract":"<div><div>This work presents some numerical and experimental validations of the free-vibration behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory (<span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span>). The <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> formulation enhances the Timoshenko's kinematics with a piece-wise zigzag cubic distribution of the axial displacement, and a smoothed parabolic variation for the transverse deflection. Simultaneously, an a-priori assumption is made for the transverse normal stress and the transverse shear one: the former is assumed to be a third-order power series expansion of the thickness coordinate, while the latter is derived through the integration of Cauchy's equations. The equations of motion and consistent boundary conditions for the free-vibration problem are derived through the Hellinger-Reissner (HR) theorem. Taking advantage of the C<sup>0</sup>-continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated, i.e., the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> element. The analytical and FE performances of the proposed <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> model are first addressed by means of a comparison with high-fidelity 3D FE models. Subsequently, an experimental campaign is conducted using LASER Doppler Vibrometry (LDV) to evaluate the modal parameters of a series of thick sandwich beams made of aluminium alloy face-sheets and Rohacell® WF110 core. The experimental results concerning the natural frequencies and modal shapes of the thick sandwich beam specimens under free-free boundary conditions are compared with those given by <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> and high-fidelity 3D FE models. The numerical-experimental assessment highlights the effect of core and face-sheet thickness on frequency estimations, as well as the complexity of reproducing in the numerical model the experimental uncertainties. In general, the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104435"},"PeriodicalIF":3.5,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144885420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-08-18DOI: 10.1016/j.finel.2025.104434
Sihua Hu , Xing Luo , Wei Xiang
This paper presents a p-version finite element framework for analyzing the thermal fracture behavior of quasi-brittle materials under coupled thermo-mechanical loadings. The proposed formulation, based on the hierarchical quadrature element method (HQEM), enables accurate capture of temperature gradients even on relatively coarse meshes. Its accuracy in simulating heat conduction and thermally induced deformation is validated against ABAQUS results.
The HQEM is integrated with the virtual crack closure method to compute fracture parameters under combined thermal and mechanical loadings, significantly reducing mesh refinement and preprocessing effort compared to conventional h-version FEM. To efficiently track complex crack paths, a minimum-increment remeshing strategy is introduced, which controls element growth while preserving the geometric accuracy of crack paths during iterative crack propagation analysis, significantly reducing the computational cost associated with frequent remeshing. Applications to four representative numerical examples demonstrate excellent agreement with existing literature, confirming the reliability and accuracy of the proposed approach for coupled thermo-mechanical fracture analysis.
{"title":"Integration of hierarchical quadrature element method with a minimum-increment remeshing strategy for simulating coupled thermo-mechanical fracture in quasi-brittle materials","authors":"Sihua Hu , Xing Luo , Wei Xiang","doi":"10.1016/j.finel.2025.104434","DOIUrl":"10.1016/j.finel.2025.104434","url":null,"abstract":"<div><div>This paper presents a <em>p</em>-version finite element framework for analyzing the thermal fracture behavior of quasi-brittle materials under coupled thermo-mechanical loadings. The proposed formulation, based on the hierarchical quadrature element method (HQEM), enables accurate capture of temperature gradients even on relatively coarse meshes. Its accuracy in simulating heat conduction and thermally induced deformation is validated against ABAQUS results.</div><div>The HQEM is integrated with the virtual crack closure method to compute fracture parameters under combined thermal and mechanical loadings, significantly reducing mesh refinement and preprocessing effort compared to conventional <em>h</em>-version FEM. To efficiently track complex crack paths, a minimum-increment remeshing strategy is introduced, which controls element growth while preserving the geometric accuracy of crack paths during iterative crack propagation analysis, significantly reducing the computational cost associated with frequent remeshing. Applications to four representative numerical examples demonstrate excellent agreement with existing literature, confirming the reliability and accuracy of the proposed approach for coupled thermo-mechanical fracture analysis.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104434"},"PeriodicalIF":3.5,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-08-15DOI: 10.1016/j.finel.2025.104420
Liyun Zuo , Guangzhi Du
This study presents two stabilized finite element methods based on local polynomial pressure projections for the mixed steady-state Navier–Stokes–Darcy problem by utilizing the equal order finite element pairs, the -- and -- element pairs, for approximating the fluid velocity, kinematic pressure and dynamic pressure, respectively. The presented stabilized methods possess many chief characteristics, for instance, parameter free, simple calculation, element level implementation. The optimal error estimates are established. Finally, some comprehensively numerical tests are reported to examine the efficiency and robustness of the proposed algorithms.
{"title":"Two stabilized finite element methods based on local polynomial pressure projection for the steady-state Navier–Stokes–Darcy problem","authors":"Liyun Zuo , Guangzhi Du","doi":"10.1016/j.finel.2025.104420","DOIUrl":"10.1016/j.finel.2025.104420","url":null,"abstract":"<div><div>This study presents two stabilized finite element methods based on local polynomial pressure projections for the mixed steady-state Navier–Stokes–Darcy problem by utilizing the equal order finite element pairs, the <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> element pairs, for approximating the fluid velocity, kinematic pressure and dynamic pressure, respectively. The presented stabilized methods possess many chief characteristics, for instance, parameter free, simple calculation, element level implementation. The optimal error estimates are established. Finally, some comprehensively numerical tests are reported to examine the efficiency and robustness of the proposed algorithms.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104420"},"PeriodicalIF":3.5,"publicationDate":"2025-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144841668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-08-14DOI: 10.1016/j.finel.2025.104418
Juan Camilo Molina-Villegas, Julián Esteban Ossa Gómez
This paper presents the formulation of the Green’s Function Stiffness Method (GFSM) for the static analysis of linearly elastic uniform Euler–Bernoulli beams on two-parameter elastic foundations subjected to arbitrary external loads. The GFSM is a mesh-reduction method closely related to the Finite Element Method (FEM) family, offering a means to compute closed-form solutions for framed structures. It is based on a strong-form formulation and decomposes the element-level response into homogeneous and fixed (particular) components, the latter obtained analytically using Green’s functions of fixed-end elements. The method retains essential FEM features — including shape functions, stiffness matrices, and fixed-end force vectors — while extending the capabilities of the Transcendental Finite Element Method (TFEM), a FEM variant that employs exact shape functions. In this context, the GFSM serves as a post-processing enhancement that transforms the approximate TFEM solution into an exact closed-form. A defining characteristic of the GFSM is that its formulation relies solely on the solution of the homogeneous form of the governing differential equations — specifically, the shape functions and stiffness matrix coefficients that constitute the core of the TFEM. The effectiveness of the GFSM is demonstrated through two examples, where its results are compared against those obtained from TFEM with varying levels of mesh refinement.
{"title":"A Green’s function driven mesh reduction technique for obtaining closed-form solutions of uniform Euler–Bernoulli beams on two-parameter elastic foundations","authors":"Juan Camilo Molina-Villegas, Julián Esteban Ossa Gómez","doi":"10.1016/j.finel.2025.104418","DOIUrl":"10.1016/j.finel.2025.104418","url":null,"abstract":"<div><div>This paper presents the formulation of the Green’s Function Stiffness Method (GFSM) for the static analysis of linearly elastic uniform Euler–Bernoulli beams on two-parameter elastic foundations subjected to arbitrary external loads. The GFSM is a mesh-reduction method closely related to the Finite Element Method (FEM) family, offering a means to compute closed-form solutions for framed structures. It is based on a strong-form formulation and decomposes the element-level response into homogeneous and fixed (particular) components, the latter obtained analytically using Green’s functions of fixed-end elements. The method retains essential FEM features — including shape functions, stiffness matrices, and fixed-end force vectors — while extending the capabilities of the Transcendental Finite Element Method (TFEM), a FEM variant that employs exact shape functions. In this context, the GFSM serves as a post-processing enhancement that transforms the approximate TFEM solution into an exact closed-form. A defining characteristic of the GFSM is that its formulation relies solely on the solution of the homogeneous form of the governing differential equations — specifically, the shape functions and stiffness matrix coefficients that constitute the core of the TFEM. The effectiveness of the GFSM is demonstrated through two examples, where its results are compared against those obtained from TFEM with varying levels of mesh refinement.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104418"},"PeriodicalIF":3.5,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Accurate simulation of the printing process is essential for improving print quality, reducing waste, and optimizing the printing parameters of extrusion-based additive manufacturing. Traditional additive manufacturing simulations are very compute-intensive and are not scalable to simulate even moderately sized geometries. In this paper, we propose a general framework for creating a digital twin of the dynamic printing process by performing physics simulations with the intermediate print geometries. Our framework takes a general extrusion-based additive manufacturing G-code, generates an analysis-suitable voxelized geometry representation from the print schedule, and performs physics-based (transient thermal) simulations of the printing process. Our approach leverages adaptive octree meshes for both geometry representation as well as for fast simulations to address real-time predictions. We demonstrate the effectiveness of our method by simulating the printing of complex geometries at high voxel resolutions with both sparse and dense infills. Our results show that this approach scales to high voxel resolutions and can predict the transient heat distribution as the print progresses. Because the simulation runs faster than real print time, the same engine could, in principle, feed thermal predictions back to the machine controller (e.g., to adjust fan speed or extrusion rate). The present study establishes the computational foundations for a real-time digital twin, which can be used for closed control loop control in the future.
{"title":"High-resolution thermal simulation framework for extrusion-based additive manufacturing of complex geometries","authors":"Dhruv Gamdha, Kumar Saurabh, Baskar Ganapathysubramanian, Adarsh Krishnamurthy","doi":"10.1016/j.finel.2025.104410","DOIUrl":"10.1016/j.finel.2025.104410","url":null,"abstract":"<div><div>Accurate simulation of the printing process is essential for improving print quality, reducing waste, and optimizing the printing parameters of extrusion-based additive manufacturing. Traditional additive manufacturing simulations are very compute-intensive and are not scalable to simulate even moderately sized geometries. In this paper, we propose a general framework for creating a digital twin of the dynamic printing process by performing physics simulations with the intermediate print geometries. Our framework takes a general extrusion-based additive manufacturing G-code, generates an analysis-suitable voxelized geometry representation from the print schedule, and performs physics-based (transient thermal) simulations of the printing process. Our approach leverages adaptive octree meshes for both geometry representation as well as for fast simulations to address real-time predictions. We demonstrate the effectiveness of our method by simulating the printing of complex geometries at high voxel resolutions with both sparse and dense infills. Our results show that this approach scales to high voxel resolutions and can predict the transient heat distribution as the print progresses. Because the simulation runs faster than real print time, the same engine could, in principle, feed thermal predictions back to the machine controller (e.g., to adjust fan speed or extrusion rate). The present study establishes the computational foundations for a real-time <em>digital twin</em>, which can be used for closed control loop control in the future.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104410"},"PeriodicalIF":3.5,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-08-13DOI: 10.1016/j.finel.2025.104416
Nima Azizi , Wolfgang Dornisch
In this paper, we propose a geometrically nonlinear spectral shell element based on Reissner–Mindlin kinematics using a rotation-based formulation with additive update of the discrete nodal rotation vector. The formulation is provided in matrix notation in detail. Additionally, we highlight the advantages of the spectral element method (SEM) in combination with Gauss–Lobatto–Legendre quadrature regarding the computational costs to generate the element stiffness matrix. To assess the performance of the new formulation for large deformation analysis, we compare it to three other numerical methods. One of these methods is a non-isoparametric SEM shell using the geometry definition of isogeometric analysis (IGA), while the other two are IGA shell formulations which differ in the rotation interpolation. All formulations base on Rodrigues’ rotation tensor. Through the solution of various challenging numerical examples, it is demonstrated that although IGA benefits from an exact geometric representation, its influence on solution accuracy is less significant than that of shape function characteristics and rotational formulations. Furthermore, we show that the proposed SEM shell, despite its simpler rotational formulation, can produce results comparable to the most accurate and complex version of IGA. Finally, we discuss the optimal SEM strategy, emphasizing the effectiveness of employing coarser meshes with higher-order elements.
{"title":"A rotation-based geometrically nonlinear spectral Reissner–Mindlin shell element","authors":"Nima Azizi , Wolfgang Dornisch","doi":"10.1016/j.finel.2025.104416","DOIUrl":"10.1016/j.finel.2025.104416","url":null,"abstract":"<div><div>In this paper, we propose a geometrically nonlinear spectral shell element based on Reissner–Mindlin kinematics using a rotation-based formulation with additive update of the discrete nodal rotation vector. The formulation is provided in matrix notation in detail. Additionally, we highlight the advantages of the spectral element method (SEM) in combination with Gauss–Lobatto–Legendre quadrature regarding the computational costs to generate the element stiffness matrix. To assess the performance of the new formulation for large deformation analysis, we compare it to three other numerical methods. One of these methods is a non-isoparametric SEM shell using the geometry definition of isogeometric analysis (IGA), while the other two are IGA shell formulations which differ in the rotation interpolation. All formulations base on Rodrigues’ rotation tensor. Through the solution of various challenging numerical examples, it is demonstrated that although IGA benefits from an exact geometric representation, its influence on solution accuracy is less significant than that of shape function characteristics and rotational formulations. Furthermore, we show that the proposed SEM shell, despite its simpler rotational formulation, can produce results comparable to the most accurate and complex version of IGA. Finally, we discuss the optimal SEM strategy, emphasizing the effectiveness of employing coarser meshes with higher-order elements.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104416"},"PeriodicalIF":3.5,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-08-13DOI: 10.1016/j.finel.2025.104428
Xin Ye , Shanzhi Liu , Weibin Wen , Pan Wang , Jun Liang
This study proposes a novel quasi-smooth manifold element (QSME) method to solve structural heat conduction problem. Compared with the conventional finite element (FE) method, the main advantage of the QSME method is the use of high-order local approximation. This ensures the continuity of first-order derivatives at element nodes, enhancing computation accuracy. The results show that the QSME method has high computation accuracy and efficiency. It can effectively solve the nonlinear thermal radiation problem of complex geometries. Under the same degrees of freedom (DOFs), the QSME method achieves at least one-order magnitude higher accuracy than the conventional FE method. Moreover, compared with the FE method, it attains faster convergence rate and requires far less DOFs to achieve the roughly same solution accuracy. This method provides an efficient computational tool for heat conduction analysis and coupled multi-physics simulations.
{"title":"A novel quasi-smooth manifold element method for structural transient heat conduction analysis with radiation and nonlinear boundaries","authors":"Xin Ye , Shanzhi Liu , Weibin Wen , Pan Wang , Jun Liang","doi":"10.1016/j.finel.2025.104428","DOIUrl":"10.1016/j.finel.2025.104428","url":null,"abstract":"<div><div>This study proposes a novel quasi-smooth manifold element (QSME) method to solve structural heat conduction problem. Compared with the conventional finite element (FE) method, the main advantage of the QSME method is the use of high-order local approximation. This ensures the continuity of first-order derivatives at element nodes, enhancing computation accuracy. The results show that the QSME method has high computation accuracy and efficiency. It can effectively solve the nonlinear thermal radiation problem of complex geometries. Under the same degrees of freedom (DOFs), the QSME method achieves at least one-order magnitude higher accuracy than the conventional FE method. Moreover, compared with the FE method, it attains faster convergence rate and requires far less DOFs to achieve the roughly same solution accuracy. This method provides an efficient computational tool for heat conduction analysis and coupled multi-physics simulations.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104428"},"PeriodicalIF":3.5,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-08-08DOI: 10.1016/j.finel.2025.104417
P. Pradhan, H. Murthy
The accuracy of FE analysis depends on the element size and integration technique used and requires significant computational effort for 3D contact problems involving large stress gradients. Therefore, contacts with similar geometries in the third dimension are typically analyzed using 2D techniques. Analysis of such 2D contacts using infinite series to solve the governing singular integral equations requires much lesser computation effort than even 2D FE analysis. However, it neglects the effect of finite dimension in the third direction due to which the contact is not under plane conditions. To investigate the effect of finiteness of third dimension in a computationally efficient manner, a hybrid technique is developed for 3D contact analysis that inherits the versatility of FE analysis and the computational efficiency of the series solution. Its results are compared to those of a detailed 3D FE analysis with fine mesh and full integration to ascertain its efficacy. They match very well in most of the contact regions except for a small difference in peak pressure near the free edge of contact.
{"title":"A computationally efficient hybrid technique for analyzing three-dimensional effects in contacts","authors":"P. Pradhan, H. Murthy","doi":"10.1016/j.finel.2025.104417","DOIUrl":"https://doi.org/10.1016/j.finel.2025.104417","url":null,"abstract":"The accuracy of FE analysis depends on the element size and integration technique used and requires significant computational effort for 3D contact problems involving large stress gradients. Therefore, contacts with similar geometries in the third dimension are typically analyzed using 2D techniques. Analysis of such 2D contacts using infinite series to solve the governing singular integral equations requires much lesser computation effort than even 2D FE analysis. However, it neglects the effect of finite dimension in the third direction due to which the contact is not under plane conditions. To investigate the effect of finiteness of third dimension in a computationally efficient manner, a hybrid technique is developed for 3D contact analysis that inherits the versatility of FE analysis and the computational efficiency of the series solution. Its results are compared to those of a detailed 3D FE analysis with fine mesh and full integration to ascertain its efficacy. They match very well in most of the contact regions except for a small difference in peak pressure near the free edge of contact.","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"51 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144900300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Variable Angle Tow (VAT) composites are advanced materials that enable spatial stiffness tailoring within the lamina through curvilinear fibre paths, in contrast to the conventional constant stiffness composites, which use straight fibre profiles. The analysis of such complex structures necessitates refined two-dimensional plate theories capable of accurately capturing their mechanical behaviour with optimal trade-off between accuracy and computational demand. This study presents static and buckling analysis of VAT composite plates using the Equivalent Single Layer (ESL)-based Higher Order Shear Deformation and Normal Theory (HOSNT12). The governing equations are solved using the finite element approach. A key novelty lies in the integration of HOSNT12 with the Gauss Point Change (GPC) strategy and its comparison with the Constant Stiffness Element (CSE) approach, including an investigation of varying Gauss point distributions. Unlike traditional ESL models, the proposed formulation captures thickness-stretching effects, making it well suited for moderately thick and thick composite plates. The study assesses the influence of fibre angle orientations on static and buckling behaviour in addition to the evaluation of the stress concentration around the central hole in VAT plates.
{"title":"Efficient finite element framework for static and buckling analysis of variable angle tow composite plates using thickness stretching kinematic model","authors":"Mohnish Kumar Sahu , Pokhraj Harshal , Prakash Chettri , Himanshu , Devesh Punera","doi":"10.1016/j.finel.2025.104415","DOIUrl":"10.1016/j.finel.2025.104415","url":null,"abstract":"<div><div>Variable Angle Tow (VAT) composites are advanced materials that enable spatial stiffness tailoring within the lamina through curvilinear fibre paths, in contrast to the conventional constant stiffness composites, which use straight fibre profiles. The analysis of such complex structures necessitates refined two-dimensional plate theories capable of accurately capturing their mechanical behaviour with optimal trade-off between accuracy and computational demand. This study presents static and buckling analysis of VAT composite plates using the Equivalent Single Layer (ESL)-based Higher Order Shear Deformation and Normal Theory (HOSNT12). The governing equations are solved using the finite element approach. A key novelty lies in the integration of HOSNT12 with the Gauss Point Change (GPC) strategy and its comparison with the Constant Stiffness Element (CSE) approach, including an investigation of varying Gauss point distributions. Unlike traditional ESL models, the proposed formulation captures thickness-stretching effects, making it well suited for moderately thick and thick composite plates. The study assesses the influence of fibre angle orientations on static and buckling behaviour in addition to the evaluation of the stress concentration around the central hole in VAT plates.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104415"},"PeriodicalIF":3.5,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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