Finite Elements in Analysis and Design最新文献

Manufacturing processes of composites involve a margin of parameter variability (e.g., geometric, mechanical, loading) which results in an inaccurate prediction of their dynamics when considered with exact assumptions. Real-time calculation of such structures confronts engineers with several challenges (e.g., dimension of finite element model, size of parameter space, uncertainty level, nonlinearity). To guarantee accuracy while saving computing time, a double-process Reduced Order Model (ROM) is proposed. It allows reducing both offline data acquisition and online data interpolation for real-time calculation. The learning phase is gradually becoming one of the most critical part of data-driven models. To overcome this problem, a set of reduced bases are built using the Proper Orthogonal Decomposition (POD) from a set of solutions computed using a regression-based Polynomial Chaos Expansion for a properly chosen Design of Experiments. In the online phase, the POD bases are interpolated on a Grassmann manifold using the Inverse Distance Weighting at a non-sampled set of the uncertain parameters’ values. The proposed double-process ROM allows to accurately approximate the nonlinear dynamics of a laminate plate with uncertain thickness and fiber orientation of two layers, with a drastically reduced computing time compared to a Full Order Model solving based on classical statistical data-sampling and postprocessing.

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.