International Journal for Numerical Methods in Engineering最新文献

Accurate stiffness and damage identification are the most important parts of structural health monitoring (SHM) for civil engineering structures. Reinforced concrete (r/c) structures are especially challenging due to the numerous cracks dispersed along the length of concrete elements. These cracks can originate from, for example, regular load of a structure, shrinkage or overloading. The usual way to tackle stiffness identification of r/c structures is to obtain the averaged linear stiffness of selected element areas through finite element model-based or response-based methods. In this paper, a variation of a weighted residual penalty-based local smoothing technique for direct stiffness identification was developed and compared to the state-of-the-art methods. The method is based on direct measurement of the axis rotations and rotational natural modes using novel MEMS rotation rate sensors. The rotational modes can be later smoothed without additional traditional translational acceleration measurements to calculate the curvature and stiffness of the beam. However, as shown in the paper, rotational modes can also be used directly for stiffness identification. The experimental analysis shows that the application of rotational measurements facilitates response-based stiffness identification of the r/c elements, providing more accurate damage identification.

This article presents a comparative study of the computational characteristics of Finite Element Analysis (FEA) and Isogeometric Analysis (IGA) in studying large elastic deformations and large-amplitude vibrations of shell-type structures. A geometrically nonlinear seven-parameter shell model is employed in a Lagrangian description in which the shell deformation is represented in mid-surface. Using a curvilinear coordinate system suitable for various geometries, the kinematic and kinetic of the problem are established, and Hamilton's principle is applied to derive the governing equations. The strain–displacement relationships and consequently, the remaining variational formulations are expressed in a matrix-vector form, allowing for direct implementation in both FEA and IGA. This efficient formulation enables a fair and consistent comparison between the two methods. Several numerical examples are examined, including the well-known static benchmark problems and their corresponding forced vibration analyses. The primary contribution of this article is the demonstration of the computational efficiency of isogeometric analysis in challenging case studies of geometrically nonlinear shells. Additional novel contributions include deriving a unified formulation for seven-parameter FEA and IGA shell models as well as analyzing the large-amplitude free and forced vibrations of shells.

This paper introduces a total-Lagrangian generalized particle domain method (TLGPDM) for explicit solid dynamics. In contrast to the updated Lagrangian generalized particle domain method (ULGPDM), TLGPDM consistently references the initial configuration throughout the computation. As a result, the basis functions and their derivatives are computed only once prior to the simulation loop, thereby substantially reducing the computational cost. In addition, a comprehensive contact algorithm is developed within the TLGPDM framework. Building upon the pinball contact algorithm, it incorporates a global search, a local search, and a refined contact force computation, thus enhancing the robustness and accuracy of contact treatment under the total-Lagrangian formulation. Four benchmark examples are presented to validate the proposed method and to assess its performance. The numerical results demonstrate that TLGPDM achieves superior computational efficiency compared with ULGPDM. Moreover, the proposed contact algorithm outperforms the conventional pinball contact algorithm in both accuracy and efficiency when applied within the TLGPDM framework.

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.