International Journal for Numerical Methods in Engineering最新文献

Soft materials, including elastomers, gels, and biological tissues, undergo extreme, complex deformations under near-incompressibility, posing significant challenges for numerical modeling. The hybrid Eulerian–Lagrangian particle-based approach, the Material Point Method (MPM), offers advantages for modeling these behaviors, but challenges remain, including prescribing essential boundary conditions, volumetric locking, cut-cell instabilities, and cell crossing errors. In this work, we introduce an extended mixed B-spline MPM that integrates subdivision-stabilized displacement–pressure interpolations with the Nitsche method for weak enforcement of essential boundary conditions. The subdivision-based mixed formulation ensures smooth, oscillation-free pressure and stress fields throughout the simulations while alleviating volumetric locking in quasi-compressible problems. The extended B-spline approach improves numerical stability at domain boundaries by mitigating ill-conditioning in the stiffness matrix, while higher-order interpolations reduce cell-crossing errors. The symmetric Nitsche method preserves the symmetry of the stiffness matrix, enabling efficient mechanical stability analysis in implicit MPM. Numerical examples—including torsional buckling, pore collapse, and soft metamaterial compression—demonstrate the method's robustness in capturing highly nonlinear mechanical responses under extreme deformations. The developed framework provides a stable and efficient particle-based approach for simulating soft materials and can be extended to multi-field coupled problems.

This paper addresses the optimal control problem of constrained mechanical systems formulated in minimal coordinates. To avoid the underlying parameterization singularity issue of minimal coordinates, we derive the equivalent maximal principle in multiple minimal coordinates. With appropriate boundary transition conditions, they actually describe the same optimal trajectories and control inputs as the differential algebraic equations (DAEs) formulation in redundant coordinates. Based on the tangent space parameterization technique, a sequence of tangent charts is built along given initial trajectories. Furthermore, the collocation method in multiple minimal coordinates is proposed. The proposed formulation is more efficient to generate high-accuracy optimal trajectories and control inputs, compared to two alternative methods in redundant coordinates. Simulations on two constrained mechanical systems verify the effectiveness of our approach.

Nonlinear structural-acoustic interaction problems are conventionally solved by time marching methods, but they are computationally expensive for obtaining multi-scale or bifurcation solutions, and are impossible to follow particular solution branches. This paper aims to develop a partitioned frequency-domain finite element method (PFD-FEM) to enhance the computational efficiency and versatility for nonlinear dynamics analysis of coupled large-deformable structure and unbounded acoustic fluid systems. In the method, all variables of the structure and finite-amplitude acoustic fluid are spatially discretized by nonlinear finite element method and temporally represented by the harmonic balance method. An arbitrary Lagrangian–Eulerian framework is adopted to update the acoustic meshes near the large-deformable structural-acoustic interface in the frequency domain. Several benchmark cases of nonlinear structural-acoustic interaction, including finite-amplitude acoustic waves radiated from large-amplitude pulsating cylinder, pulsating sphere, vibrational beam, and vibrational plate, are used to validate the PFD-FEM. Convergence studies are performed in these cases. Compared to time marching methods, nonlinear structural and acoustic responses as well as the contribution of different frequency components can be quickly and directly obtained by the proposed PFD-FEM.

Tension-compression asymmetry (TCA) significantly influences the mechanical behavior and optimal designs, ranging from concrete to advanced composites. This study develops bi-modulus Euler-Bernoulli beam element formulations employing the integration of cross-sectional constitutive relations, according to the partitioning of tension and compression states. Both displacement-based and force-based elements are formulated, with the latter accurately capturing the neutral surface. An analysis framework for bi-modulus frame structures is then proposed, enabling stable and efficient solutions for large-scale problems with a wide-range TCA. Numerical examples confirm the significant influence of TCA on structural responses and validate the proposed framework. Furthermore, a ground-structure-based optimization procedure is presented for single- and two-phase bi-modulus frame structures, revealing how TCA profoundly impacts optimal designs. These findings highlight the consideration of TCA for more efficient material utilization and novel structural designs, providing valuable insights for future engineering applications.

In 2021, following the successful launch of the Tianhe-Core-Module, the large-scale flexible solar array was deployed smoothly in orbit, marking China's first application of flexible solar arrays and subsequently establishing them as a prominent research focus. The substrate of the flexible solar array is composed of polyimide composites, a typical polymer material that exhibits viscoelastic-viscoplastic behavior under on-orbit fluctuating thermal-mechanical action, thereby influencing the long-term structural performance. This study begins by investigating the nonlinear viscoelastic-viscoplastic behavior of the flexible substrate through creep-unloading-recovery experiments under varying temperatures and stress levels. Subsequently, a coupled viscoelastic-viscoplastic constitutive model is proposed. For the viscoelastic component, a novel generalized double hereditary integral model is developed based on the microelement method. For the viscoplastic component, a nonlinear time-dependent evolution model, independent of the yield surface, is formulated to account for the unique characteristics of the substrate. A detailed methodology for calibrating all nonlinear parameters through experimental data is provided. Furthermore, leveraging the finite element incremental approach, an innovative dual-recursive numerical scheme and a nonlinear iterative-correction computational scheme are implemented, incorporating the model's distinctive features. The nonlinear viscoelastic-viscoplastic Jacobian tensor is rigorously derived, and a user-defined material subroutine (UMAT) is developed to facilitate large-scale numerical simulations. Finally, the accuracy, reliability, and generality of the proposed method are validated through comparative analyses with experimental data, published literature, the linear Boltzmann hereditary integral model, and the nonlinear Schapery hereditary integral model. The findings of this study will contribute to the evaluation of the long-term in-orbit behavior of flexible solar arrays.

A novel numerical computation technique called the Chebyshev-matrix collocation method is proposed. The method is based on the Chebyshev polynomials of the second kind and collocation points. The new approach is first applied to vibration models of non-uniform (i.e., tapered) Euler–Bernoulli beams. The non-dimensional equation of motion for transverse vibration of a non-uniform Euler–Bernoulli beam is presented in a general form. With the general expression, different types of non-uniform beams can be modeled by changing the parameters related to non-uniform geometry. The Chebyshev-matrix collocation algorithm is described using a detailed flow chart. The algorithm makes it possible to obtain solutions with alternative support combinations. The solution algorithm is applied to three different non-uniformity cases of Euler–Bernoulli beams: tapered height and constant width; tapered width and height; and constant thickness with decreasing width. Transverse vibration responses are presented for simple-simple, clamped-clamped, and clamped-free support conditions. The natural frequencies are obtained, and mode shapes are plotted for all cases. The residual error analyses are proposed to demonstrate the accuracy of the new approach. The results are compared with exact solutions to prove the validity of the proposed method.

Flexoelectricity, an electromechanical coupling phenomenon induced by strain gradients, finds plate structures to be particularly suitable due to their inherent susceptibility to developing such gradients. However, practical exploitation requires efficient numerical tools for modeling geometrically complex thin-walled structures. This work presents a novel 4-node quadrilateral Trefftz element for analyzing flexoelectric thin plates within consistent couple stress theory (CCST). To accomplish this, the non-classical flexoelectric Kirchhoff plate model is first established based on CCST, and Trefftz functions satisfying the governing equations are systematically derived. These Trefftz functions subsequently serve as basis functions for constructing the displacement field, and generalized conforming conditions at collocation points are used to link them to nodal degrees of freedom. The performance of the proposed element is rigorously evaluated through benchmark problems involving static bending and free vibration analyses. Numerical results are compared against analytical solutions or three-dimensional finite element simulations. It is shown that the element achieves high precision in capturing the size-dependent flexoelectric responses, which are prominent at the micro/nano-scale, and exhibits superior robustness against mesh distortion. This establishes the method as an efficient numerical tool for the design of flexoelectric plates, such as those used in micro-sensors and energy harvesters.

In this paper, we consider the transmission model of elastic waves, where the bounded elastic bodies are anisotropic. By utilizing the Dirichlet-to-Neumann operator to truncate the unbounded physical domain, we can solve the transmission problem via the finite element discretization in a bounded domain. To improve computational efficiency for non-smooth boundaries, we establish a residual-based a posteriori error estimate for the Dirichlet-to-Neumann finite element method and develop an adaptive algorithm. Numerical experiments demonstrate that the proposed adaptive algorithm can significantly improve the computational efficiency.

This study investigates the failure mechanisms of spur gears under bending fatigue loading, focusing on crack initiation, propagation paths, and stress field distribution. Finite element simulations are conducted to obtain linear elastic stress–strain data at the tooth root, which are then incorporated into the Smith-Watson-Topper (SWT) multi-axial fatigue model to predict the crack initiation location. Subsequently, a moving contact load model with time-dependent magnitude and direction is developed through the secondary implementation of an Abaqus DLOAD user subroutine using Fortran programming. During crack propagation analysis, variations in stress intensity factors (SIF), crack propagation paths, and stress field distribution are examined, whereas the NASGRO model is applied to estimate fatigue life under different operating conditions. The results indicate that the predicted fatigue life under moving contact load closely matches experimental values. During crack propagation, merging cracks lead to interactions and overlapping of stress fields, which ultimately reach a new equilibrium after merging. Furthermore, compared to loading at the highest position of single-tooth contact (HPSTC), the dynamic effect of the moving contact load effectively alleviates stress concentration and reduces the crack propagation rate.