Archive of Applied Mechanics最新文献

In this paper, a formulation of reduced-order finite element (FE) model is presented for geometrically nonlinear dynamic analysis of viscoelastic structures based on the fractional-order derivative constitutive relation and harmonic balance method. The main focus is to formulate the nonlinear reduced-order models (ROMs) in the time and frequency domain without involving the corresponding full-order FE models, and it is carried out by means of a special factorization of the nonlinear strain–displacement matrix. Furthermore, a methodology for the enrichment of reduction basis (RB) over that obtained from conventional approaches is presented where the proper orthogonal decomposition method is utilized by comprising the correlation matrix as the union of stiffness-normalized reduction basis vectors and the corresponding static derivatives. The results reveal a significantly reduced computational time due to the formulation of the nonlinear ROMs without involving the full-order FE model. A good accuracy of the nonlinear ROMs of viscoelastic structures is also achieved through the present method of enrichment of RB.

The mechanic-electro coupling overlapping finite element method (OFEM) is proposed to improve the accuracy in solving the mechanical characteristics of piezoelectric structures. Based on the basic equations and boundary conditions of piezoelectric materials, overlapping triangle elements are used to discretize the solution domain of piezoelectric structures, and the displacement function and potential function of the mechanic-electro coupling OFEM are constructed through local interpolation. The control equation of the mechanic-electro coupling OFEM is derived using the variation principle. The accuracy and validity of this method are verified by comparing with the reference solution and analytical solution in patch test and piezoelectric patch bending test. The static characteristics of the cantilever-typed piezoelectric sensor model, the rectangular plate with one-sided piezoelectric patch configuration, and the hole-containing piezoelectric energy harvester model are analyzed. The mechanic-electro coupling OFEM has high engineering value and broad application prospects in analyzing the structural mechanical properties of intelligent piezoelectric components.

This paper dealt with the vibration characteristics of an auxetic rectangular plate under in-plane compression. Firstly, the equivalent bending stiffness matrix of a star-shaped auxetic plate was obtained using Castigliano's theorem and the homogenization technique. Then, employing the classical plate theory (CPT) in conjunction with the Rayleigh–Ritz method, the natural frequencies of auxetic plate were extracted. The chebyshev polynomial series has been selected to define the assumed displacement fields of the plate. Convergence study for the Rayleigh–Ritz method was conducted. The accuracy of the proposed mathematical model for the star-shaped auxetic plate was validated using the results from a finite element analysis (FEA). Effects of unit cell geometric parameters on the natural frequencies of the plate were examined. The auxeticity angle of star-shaped pattern had a significant effect on the natural frequencies. The present approach can be extended into other auxetic patterns, such as re-entrant bowtie auxetics.

Based on the surface elasticity theory combined with the theories of Kirchhoff plate and Mindlin plate, the influences of surface effects on the buckling and post-buckling behaviors of nano-laminates are studied. Analytical solutions for critical buckling loads under uniaxial and biaxial compressions are obtained. Furthermore, approximate solutions for critical post-buckling loads under moveable and immoveable edge conditions are provided by using the Galerkin’s method. Numerical examples are given to study the influences of thickness, number of layers, surface parameters and the length of the nano-laminates on buckling and post-buckling critical loads. Results obtained indicate that the surface/interface energy is connected with the number of layers. In addition, the effects of the surface/interface energy on the critical loads enhance through increasing the length of the laminates but reduce by increasing the thickness. Mechanical model, analytical method and conclusions of this work are helpful for designing and examining the stability of the nano-laminates and nanoscale devices.

A theoretical model was established to investigate the interaction between hydrogen clusters and edge dislocations emitted from a semi-elliptical surface crack tip in deformed nanometallic materials. The model’s solution was obtained by using the complex method, and the influence of the concentration and location of hydrogen clusters, temperature, crack shape, material constants, and the dislocation emission angle on the critical stress intensity factor (SIFs) corresponding to the first dislocation emission from crack tips was investigated through numerical analysis. The results show that dislocations are easily emitted from the crack tip at high hydrogen concentration, and hydrogen clusters close to the crack tip will hinder the emission of dislocations from its crack tip. When considering the influence of hydrogen cluster, an increase in temperature, an extension of crack length or an increase in crack tip curvature radius can all make the emission of dislocations at the crack tip difficult, thereby reducing the toughness of the material caused by dislocation emission.

In computational fluid dynamics, controlling grid scale is efficiently managed using the Advancing Front Technique (AFT). However, achieving grid generation convergence within a three-dimensional (3D) computational domain remains challenging, primarily due to excessive intersection judgments that significantly reduce efficiency. This paper addresses the non-convergence issues inherent in the 3D AFT and proposes preliminary solutions to enhance algorithm robustness while reducing intersection judgments. We introduce two neural networks trained on the backpropagation (BP) algorithms, Line-ANN and Plane-ANN, specifically designed for integration with AFT. These networks are individually combined with traditional 3D AFT to develop two enhanced methods. We assess these methods by comparing grid quality and time consumption against traditional AFT approaches. The results demonstrate that integrating Plane-ANN and Line-ANN with AFT improves overall efficiency by approximately 55% and 36%, respectively, thereby significantly enhancing grid generation efficiency.

In computational homogenization approaches, data-driven methods entail advantages due to their ability to capture complex behavior without assuming a specific material model. Within this domain, constitutive model-based and model-free data-driven methods are distinguished. The former employ artificial neural networks as models to approximate a constitutive relation, whereas the latter directly incorporate stress–strain data in the analysis. Neural network-based constitutive descriptions are one of the most widely used data-driven approaches in computational mechanics. In contrast, distance-minimizing data-driven computational mechanics enables substituting the material modeling step entirely by iteratively obtaining a physically consistent solution close to the material behavior represented by the data. The maximum entropy data-driven solver is a generalization of this method, providing increased robustness concerning outliers in the underlying data set. Additionally, a tensor voting enhancement based on incorporating locally linear tangent spaces enables interpolating in regions of sparse sampling. In this contribution, a comparison of neural network-based constitutive models and data-driven computational mechanics is made. General differences between machine learning, distance minimizing, and entropy maximizing data-driven methods are explored. These include the pre-processing of data and the required computational effort for optimization as well as evaluation. Numerical examples with synthetically generated datasets obtained by numerical material tests are employed to demonstrate the capabilities of the investigated methods. An anisotropic nonlinear elastic constitutive law is chosen for the investigation. The resulting constitutive representations are then applied in structural simulations. Thereby, differences in the solution procedure as well as use-case accuracy of the methods are investigated.

This paper aims to present an analysis of the thermo-elastoplastic bending behavior of skew functionally graded (FG) sandwich plates resting on a Winkler/Pasternak foundation, employing a novel three-dimensional (3D) meshless approach. The material properties are assumed to be completely temperature-dependent, and the sandwich plate with FG face sheets and core is exposed to mechanical and thermal loads. The discretized equation systems of nonlinear transient heat conduction and incremental thermo-elastoplasticity are derived using a 3D radial basis reproducing kernel particle approach. The meshless model utilizes a novel high-order kernel that combines Gaussian and cosine functions. The incremental plastic deformation is modeled by the Prandtl–Reuss flow rule along the isotropic hardening von Mises criterion. The results demonstrate excellent agreement when compared with those existing in the literature. The influence of different foundation parameters, skew angles, layer thickness ratios, thickness-to-length ratios, power law exponents, and boundary conditions on the elastoplastic bending behavior of the FG skew sandwich plate is evaluated.

This contribution discusses the influence of different barrier update strategies on the performance and robustness of an interior point algorithm for single-crystal plasticity at small strains. To this end, single-crystal plasticity is first briefly presented in the framework of a primal-dual interior point algorithm to outline the general algorithmic structure. The manner in which the barrier parameter is modified within the interior point method, steering the penalization of constraints, plays a crucial role for the robustness and efficiency of the overall algorithm. In this paper, we compare and analyze different strategies in the framework of crystal plasticity. In a thorough analysis of a numerical example covering a broad range of settings in monocrystals, we investigate robust hyperparameter ranges and identify the most efficient and robust barrier parameter update strategies.