Computer Methods in Applied Mechanics and Engineering最新文献

In practical engineering, a multi-input-multi-output (MIMO) structure generally features a significant number of correlated input parameters and output responses. Sensitivity analysis is usually adopted to select key parameters for improving the computational efficiency of structural analysis and design processes. Traditional sensitivity analysis methods based on probabilistic models for MIMO structures may not reliably and efficiently derive the sensitivity indexes of correlated input parameters with limited samples. To solve the above problems, a novel sensitivity analysis method for MIMO structures considering non-probabilistic correlations is proposed to estimate the influence of uncertainties and correlations among the parameters on the responses in a unified framework. Firstly, a multidimensional parallelepiped (MP) model is employed to quantify the uncertainties and non-probabilistic correlations among the parameters. A new non-probabilistic variance propagation equation based on the MP model is then proposed to derive the non-probabilistic variances of output responses. The non-probabilistic independent, correlated, and total sensitivity indexes of each parameter for multi-input-single-output (MISO) structures are defined according to the non-probabilistic variance contribution rates. A dimensional normalization method and a vector projection method are then adopted to extend the non-probabilistic sensitivity indexes of each parameter for MIMO structures with correlations. Two numerical examples and an experimental example are exemplified to verify the proficiency and efficiency of the currently proposed method.

The identification of geomaterial properties is costly but pivotal for engineering design. A wide range of approaches perform well with sufficiently measured data but their performance is problematic for sparse data. To address this issue, this study proposes an active learning based multi-fidelity residual Gaussian process (AL-MR-GP) modelling framework. A low-fidelity (LF) prediction model is first trained using extensive LF data collected from worldwide sites to generate preliminary estimations. Subsequent training employs active learning to prioritize high-fidelity data from the specific site of interest with larger information gain for calibrating the LF model to make ultimate predictions. The compression index of clays is selected as an example to examine the capability of the proposed framework. The results indicate that using the same number of site-specific datasets, the compression index of clays can be well captured by AL-MR-GP, exhibiting superior accuracy and reliability than models without incorporating multi-fidelity data or active learning. Based on unified LF data, the proposed framework becomes data-efficient for the model development of three sites and is significantly competitive in extrapolation, compared with site-specific models even with active learning. These promising characteristics indicate substantial potential to be extended to broader applications in geotechnical engineering.

We propose a parameter-free and locking-free enriched Galerkin method of arbitrary order for solving the linear elasticity problem in both two and three space dimensions. Our method uses an approximation space that enriches the vector-valued continuous Galerkin space of order $k$ with some discontinuous piecewise polynomials. To the best of our knowledge, it extends the locking-free enriched Galerkin space in Yi et al. (2022) to high orders for the first time. Compared to the continuous Galerkin method, the proposed method is locking-free with only $k^{d-1}$ additional degree of freedom on each element. The parameter-free property of our method is realized by integrating the enriched Galerkin space into the framework of the modified weak Galerkin method. We rigorously establish the well-posedness of the method and provide optimal error estimates for the compressible case. Extensive numerical examples confirm both the accuracy and the locking-free property of the proposed method.

Fluid–structure-interaction (FSI) phenomena are widely concerned in engineering practice and challenge current numerical methods. In this article, the finite element method is strongly coupled with the multi-material arbitrary Lagrangian–Eulerian (MMALE) method to develop a monolithic FSI method named the immersed multi-material arbitrary Lagrangian–Eulerian finite element method (IALEFEM). By immersing the finite elements in the MMALE computational grid, the fluid–solid interface is directly tracked by the element boundary with accurate normal directions. The fluid–structure-interaction is implicitly implemented by assembling the nodal variables and updating the Lagrangian momentum equation on the MMALE grid. Combining the advantages of both MMALE and FEM with the immersed boundary method, the IALEFEM is effective for solving complicated FSI problems with multi-material fluid flow. A slip fluid–structure-interaction method is also proposed to enhance the computational accuracy in simulating FSI problems with significantly different velocity fields. The accuracy and effectiveness of the IALEFEM are verified and validated by several benchmark numerical examples including the shock-cylinder obstacle interaction, flexible panel deformation induced by shock wave, dam break problem with large structural deformation, water entry of a wedge, fragmentation of a cylinder shell induced by blast, response of elastic plate subjected to spherical near-field explosion and structural damage of open-frame building under blast loading.

We construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane potential of the Hodgkin–Huxley ionic model. The underlying non-linearity of the Hodgkin–Huxley dynamical system, the stiffness of its solutions, and the threshold dynamics depending on the intensity of the applied current, are some of the challenges to address when exploiting artificial neural networks to learn this class of complex operators. By properly designing these operator learning techniques, we demonstrate their ability to effectively address these challenges, achieving a relative $L^2$ error as low as 1.4% in learning the solutions of the Hodgkin–Huxley ionic model.

Earthquake-induced geohazards are natural disasters that have the potential to cause severe damage to infrastructure and endanger human lives. To mitigate these natural disasters, advanced computational methods capable of dealing with large deformation and failure of geomaterials have been developed for years. Among those methods, the Smoothed Particle Hydrodynamics (SPH) method has been demonstrated to offer great flexibility in handling a wide range of challenging geotechnical problems, involving large deformations and post-failure behaviour of geomaterials. However, despite some primary attempts, a proper SPH framework for modelling seismic responses has not yet been fully developed. One of the key reasons for this is the absence of appropriate SPH boundary conditions for wave propagation analysis in infinite porous media. To overcome this problem, this study proposed new SPH boundary conditions to enable the SPH method to efficiently analyse seismic responses of geomechanics problems with compliant-base and free-field boundary conditions, allowing successfully reproducing wave propagation and dissipation in an infinite ground domain. Comprehensive verification and validation of the SPH framework, integrated with the newly developed boundary conditions, demonstrate its effectiveness in simulating the earthquake-induced large deformations and failures of geotechnical engineering problems. This suggests that the proposed computational model offers a robust tool for predicting and understanding the seismic response and associated large deformations, thereby advancing applications in geotechnical engineering and disaster risk mitigation.

This paper proposes a numerical scheme for the approximation of the solution of the Stokes or steady Navier–Stokes system for fluids with heterogeneous viscosity (generic bounded viscosity or shear thinning fluids). The scheme is based on a velocity–pressure splitting resembling a Uzawa approach combined with a grad-div stabilizing term. We establish the validity, convergence and a priori estimates for this strategy. A simpler mixed approach is also presented and studied. Numerical tests using a manufactured solution are provided, giving estimates for the accuracy order and sensitivity to the stabilizing coefficient. For more realistic numerical experiments, we present results for the lid-driven cavity.

This work integrates the immersed isogeometric analysis (IGA) with topology optimization (IITO), which paves the way of seamless integration between CAD and CAE as well as topology optimization for complex engineering structures. A truncated hierarchical B-spline (THB) based local adaptivity strategy is proposed to improve the integral accuracy of trimmed elements for immersed IGA, and an adaptive IITO framework is established in terms of the explicit elemental stiffness representation using multi-level Bézier extraction operator and tensor product decomposed implicit filter, as well as the suitably graded THB constraint. Numerical examples indicates that the proposed adaptive IITO method is superior to both traditional IITOs with adaptive Gaussian quadrature rule and successive global refinement, and achieves a sound balance between optimization accuracy and computation efficiency, irrespectively of the physical dimension and boundary conditions as well as geometry shape of design domain. Moreover, an object-oriented IITO engineering software is developed by C++ language and can be applied in engineering topology optimization design problems effectively, which show the superiorities of our IITO system. Therefore, the proposed IITO framework is a very promising way of implementing the seamless integration between CAD and CAE as well as topology optimization for complex engineering problems.

The integration of topology optimization and additive manufacturing (AM) offers a transformative approach to designing and fabricating complex structures across various industries. This synergy enables engineers to produce lightweight, high-performance designs with intricate, organic geometries that push the boundaries of conventional manufacturing methods. However, printing large 3D objects that exceed the allowable build volume of an AM machine poses a significant challenge. This necessity has led to the development of methodologies such as part decomposition (PD) to fit these objects within the build volume constraint. Previous studies have contributed to solving PD problems, but several limitations, such as the use of Euler angle representation and the lack of practical decomposed designs, need to be addressed. To the best of the authors’ knowledge, this is the first paper to develop a 3D decomposition optimization methodology for topology-optimized structures by establishing a novel rotational system and modeling joint mechanical properties. The novel rotational system, using a non-unit quaternion representation, is established to eliminate the singularity issue inherent in the Euler angle representation. This approach also allows for the effective optimization of partitioning cuboids, which represent the allowable AM build volume, by removing the unit-length constraint. Additionally, the joint mechanical properties at the interface between decomposed parts are modeled using geometrically represented hollow cuboids. Furthermore, analytical sensitivity expressions with respect to new design variables, including explicit variables of partitioning cuboids and rotation variables of non-unit quaternions, are derived and numerically verified to efficiently solve the decomposition optimization problem. Through practical case studies, the 3D decomposition optimization methodology demonstrates its effectiveness under various conditions, including varying maximum allowable AM build volumes, different initial partitioning cuboid layouts, and various joint mechanical properties.

This paper presents a dynamic formulation for the simulation of nearly incompressible structures using a mixed finite element method with equal-order interpolation pairs. Specifically, the nodal unknowns are the displacement and the volumetric strain component, something that makes possible the reconstruction of the complete stain at the integration point level and thus enables the use of strain-driven constitutive laws. Furthermore, we also discuss the resulting eigenvalue problem and how it can be applied for the modal analysis of linear elastic solids. The article puts special emphasis on the stabilisation technique used, which becomes crucial in the resolution of the generalised eigenvalue problem. In particular, we prove that using a variational multiscale method assuming the sub-grid scales to lie in the finite element space orthogonal to that of the approximation, namely the Orthogonal Sub-Grid Scales (OSGS), results in a convenient linear and symmetric generalised eigenvalue problem. The correctness, convergence and performance of the method are proven by solving a series of two- and three-dimensional examples.