Finite Elements in Analysis and Design最新文献

A two-level version for a recent semi-hybrid-mixed finite element approach for modeling Stokes and Brinkman flows is proposed. In the context of a domain decomposition of the flow region $\Omega$, composite divergence-compatible finite elements pairs in $H(\mathrm{div},\Omega )\times L^2\left(\Omega \right)$ are utilized for discretizing velocity and pressure fields, using the same approach previously adopted for two-level mixed Darcy and stress mixed elasticity models. The two-level finite element pairs of spaces in the subregions may have richer internal resolution than the boundary normal trace. Hybridization occurs by the introduction of an unknown (traction) defined over element boundaries, playing the role of a Lagrange multiplier to weakly enforce tangential velocity continuity and Dirichlet boundary condition. The well-posedness of the method requires a proper choice of the finite element space for the traction multiplier, which can be achieved after a proper velocity FE space enrichment with higher order bubble fields. The method is strongly locally conservative, yielding exact divergence-free velocity fields, demonstrating pressure robustness, and facilitating parallel implementations by limiting the communication of local common data to at most two elements. Easier coupling strategies of finite elements regarding different polynomial degree or mesh widths are permitted, provided that mild mesh and normal trace consistency properties are satisfied. Significant improvement in computational performance is achieved by the application of static condensation, where the global system is solved for coarse primary variables. The coarse primary variables are a piecewise constant pressure variable over the subregions, velocity normal trace and tangential traction over subdomain interfaces, as well as a real number used as a multiplier ensuring global zero-mean pressure. Refined details of the solutions are represented by secondary variables, which are post-processed by local solvers. Numerical results are presented for the verification of convergence histories of the method.

This work comprehensively investigates key parameters associated with a recently proposed non-intrusive coupling strategy for multiscale structural problems. The IGL-GFEM^gl combines the Iterative Global Local Method and the Generalized Finite Element Method with global–local enrichment, GFEM^gl. Different scales of the problem are solved using distinct finite element codes: the commercial software Abaqus and a research in-house code. An Iterative Global–Local non-intrusive algorithm is employed to couple the solutions provided by the two solvers, with the process accelerated by Aitken’s relaxation. Slight modifications have been introduced, and the resulting accuracy and computational performance are discussed using numerical examples. The problems investigated explore the coupling strategy within the context of 2D linear elastic problems, which include voids and crack propagation described at the local scale solved by the in-house code. A noteworthy trade-off between reducing iterations and increasing the time to solve the local problems is observed. Despite the high accuracy achieved, the two versions of the coupling strategy, namely the monolithic and staggered algorithms, exhibit different computational performances when the GFEM^gl parameters, such as the number of global–local cycles and the size of the buffer zone, are evaluated for the crack propagation simulation.

Deep energy method (DEM) has shown its successes to solve several problems in solid mechanics recently. It is known that determining proper integration scheme to precisely calculate total potential energy (TPE) value is crucial to achieve high-quality training performance of DEM but it has not been discovered satisfactorily in previous related works. To shed light on this matter, this study focuses on investigating the application of Gauss–Legendre (GL) quadrature rule in training DEM to solve one-dimensional (1D) solid mechanics problems. The technical idea of this work is (1) to design a theoretical polynomial regression (PR) model via Taylor series expansion that could well-approximate multi-layer perceptron (MLP) output and its derivatives for fully capturing the representation of DEM solution, and then (2) to extract the polynomial order of the TPE loss function via the devised PR to calculate the necessary number of GL points for training DEM. To do so, mathematical analyses are firstly developed to find out the representability of DEM for geometrically nonlinear beam bending problem as a case study and the convergence of the alternative PR to the MLP with tanh activation function, providing theoretical foundations for utilizing the PR to take the place of DEM network. Subsequently, minimum number of GL points are analytically extracted and a technical framework for estimating the maximin required GL points is devised to accurately compute the TPE loss function for ensuring DEM training convergence. Several 1D linear and nonlinear beam bending examples using both Euler–Bernoulli (EB) and Timoshenko theories with various types of boundary conditions (BCs) are selected to examine the proposed method in practice. The numerical results validate the preciseness of the developed theory and the empirical effectiveness of the devised framework.

Several methods have been developed to model the dynamic behavior of saturated porous media. However, most of them are suitable only for small strain and small displacement problems and are built in a monolithic way, so that individual improvements in the solution of the solid or fluid phases can be difficult. This study shows a macroscopic approach through a partitioned fluid–solid coupling, in which the skeleton solid is considered to behave as a Neo-Hookean material and the interstitial flow is incompressible following the Stokes–Brinkman model. The porous solid is numerically modeled with a total Lagrangian position-based finite element formulation, while an Arbitrary Lagrangian-Eulerian stabilized finite element approach is employed for the porous medium flow dynamics. In both fields, an averaging procedure is applied to homogenize the problem, resulting in a macroscopic continuous phase. The solid and fluid homogenized domains are overlapped and strongly coupled, based on a block-iterative solution scheme. Two-dimensional simulations of wave propagation in saturated porous media are employed to validate the proposed formulation through a comprehensive comparison with analytical and numerical results from the literature. The analyses underscore the proposed formulation as a robust and precise modular approach for addressing dynamic problems in poroelasticity.

This paper presents a Chimera approach for the thermal problems in welding and metallic Additive Manufacturing (AM). In particular, a moving mesh is attached to the moving heat source while a fixed background mesh covers the rest of the computational domain. The thermal field of the moving mesh is solved in the heat source reference frame. The chosen framework to couple the solutions on both meshes is a non-overlapping Domain Decomposition (DD) with Neumann–Dirichlet transmission conditions.

Increased steadiness and accuracy within the vicinity of the Heat Affected Zone (HAZ) are the main advantages of this approach. The steadiness gain allows for the use of larger time steps, which is vital in AM applications and, in particular, Laser Powder Bed Fusion (LPBF), where the disparity of time scales represents a major hurdle. Moreover, enhanced accuracy can be observed in the resulting morphology of the melt pool. It will be shown that the method addresses classical shortcomings pointed out by Goldak without requiring the use of an asymmetrical heat source profile.

A novel approach for the solution of linear elasticity problems is introduced in this communication, which uses a hybrid chimera-type technique based on both finite element and improved element-free Galerkin methods. The proposed overset improved element-free Galerkin-finite element method (Ov-IEFG-FEM) for linear elasticity uses the finite element method (FEM) throughout the entire problem geometry, whereas a fine distribution of overlapping nodes is used to perform higher order approximations via the improved element-free Galerkin (IEFG) technique in regions demanding more computational accuracy. The method relies on keeping the FEM-based results in those regions where low order of approximation is enough to provide the required accuracy, i.e. outside the region where the solution will be enriched via the IEFG technique. The overlapping domains perform an iterative transfer of kinematics information through well-defined immersed boundaries, and a detailed explanation on this regard is also presented in this communication. The Ov-IEFG-FEM is used in a set of increasingly complex linear elasticity problems, and the outcomes demonstrate the suitability and reliability of this technique to solve such problems in an accurate and remarkably simple manner.

Metal-ceramic composites by their nature have thermal residual stresses at the micro-level, which can compromise the integrity of structural elements made from these materials. The evaluation of thermal residual stresses is therefore of continuing research interest both experimentally and by modeling. In this study, two functionally graded aluminum alloy matrix composites, AlSi12/Al₂O₃ and AlSi12/SiC, each consisting of three composite layers with a stepwise gradient of ceramic content (10, 20, 30 vol%), were produced by powder metallurgy. Thermal residual stresses in the AlSi12 matrix and the ceramic reinforcement of the ungraded and graded composites were measured by neutron diffraction. Based on the X-ray micro-computed tomography (micro-XCT) images of the actual microstructure, a series of finite element models were developed to simulate the thermal residual stresses in the AlSi12 matrix and the reinforcing ceramics Al₂O₃ and SiC. The accuracy of the numerical predictions is high for all cases considered, with a difference of less than 5 % from the neutron diffraction measurements. It is shown numerically and validated by neutron diffraction data that the average residual stresses in the graded AlSi12/Al₂O₃ and AlSi12/SiC composites are lower than in the corresponding ungraded composites, which may be advantageous for engineering applications.

An intrusive Reduced Order Model (ROM) is developed for nonlinear porous media flow problems with transient and time-discontinuous fluid injection rates. The proposed ROM is significantly more computationally efficient than the Full Order Model (FOM). The training regime is generated using the FOM with constant injection rates during the offline stage. The trained ROM exhibits high accuracy for complex pumping schedules (rate vs time) simulated online. The proposed ROM uses the combination of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method (POD-DEIM), which is compared with the classical POD-Galerkin. The use of an approximated column-reduced Jacobian is shown to be vital to achieving a substantial speedup of ROM vs FOM run-times. An analysis of the trade-off between accuracy and run-time is conducted for ROMs of different sizes and hyper-parameters. The impact of the training regime on the performance of the presented ROM is assessed. The performance of the ROM is studied in the context of a two-dimensional analysis of time-varying injection into a two-well system in a layered porous media reservoir. The accuracy and efficiency of POD-DEIM motivate its potential use as a surrogate model in the real-time control and monitoring of fluid injection processes.

Wave propagation in elastodynamic problems in solids often requires fine computational meshes. In this work we propose to combine stabilized finite element methods (FEM) with an artificial neural network (ANN) correction term to solve such problems on coarse meshes. Irreducible and mixed velocity–stress formulations for the linear elasticity problem in the frequency domain are first presented and discretized using a variational multiscale FEM. A non-linear ANN correction term is then designed to be added to the FEM algebraic matrix system and produce accurate solutions when solving elastodynamics on coarse meshes. As a case study we consider acoustic black holes (ABHs) on structural elements with high aspect ratios such as beams and plates. ABHs are traps for flexural waves based on reducing the structural thickness according to a power-law profile at the end of a beam, or within a two-dimensional circular indentation in a plate. For the ABH to function properly, the thickness at the termination/center must be very small, which demands very fine computational meshes. The proposed strategy combining the stabilized FEM with the ANN correction allows us to accurately simulate the response of ABHs on coarse meshes for values of the ABH order and residual thickness outside the training test, as well as for different excitation frequencies.

A generalized finite element beam with an embedded rotation discontinuity coupled with a 3D macroelement is proposed to assess, till complete failure (no stress transfer), the vulnerability of symmetrically reinforced concrete frame structures subjected to static (monotonic, cyclic) or dynamic loading. The beam follows the Timoshenko beam theory and its sectional behavior is described in terms of generalized forces and generalized strains. The beam response up to the peak is described by a macroelement, based on plasticity theory, that adopts a 3D failure criterion expressed in terms of axial force, shear force and bending moment. The Embedded Finite Element Method is then adopted to reproduce bending dominated failure, with a global cohesive model that links the cohesive moment to a rotational jump. The formulation allows for remedy of localization phenomena and significant reduction of the necessary computational time. The performance of the proposed simplified strategy is illustrated by comparison with experimental results.