International Journal for Numerical Methods in Engineering最新文献

The effective inclusion of a priori knowledge when embedding known data in physics-based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics-constrained data-driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first-principles theory and sensor-based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy-informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data-embedding term serves as residual-based least-squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low- and high-order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary-value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.

In the present work the geometrically exact beam model is formulated in terms of unit quaternions. A projection-based discretization approach is proposed which is based on a normalization of the quaternion approximation. The discretization relies on NURBS shape functions and, alternatively, on Lagrangian interpolation. The redundancy of the quaternions is resolved by applying the method of Lagrange multipliers. In a second step the Lagrange multipliers are eliminated circumventing the need to solve saddle point systems. The resulting finite elements retain the objectivity of the underlying beam formulation. Optimal rates of convergence are observed in representative numerical examples.

A strategy that combines the global-local version of the generalized finite element method (GFEM$��{\hspace{0.17em}}^{�\text{gl}�}�$) with a mixed-dimensional coupling iterative method is proposed to simulate two-dimensional crack propagation in structures globally represented by Timoshenko-frame models. The region of interest called the local problem, where the crack propagates, is represented by a 2D elasticity model, where a fine mesh of plane stress/strain elements and special enrichment functions are used to describe this phenomenon accurately. A model of Timoshenko-frame elements simulates the overall behavior of the structure. A coarse mesh of plane stress/strain elements provides a bridge between these two representation scales. The mixed-dimensional coupling method imposes displacement compatibility and stress equilibrium at the interface between the two different element types by an iterative procedure based on the principle of virtual work. After establishing the constraint equations for the interface, the 2D elasticity model is related to the small-scale model by the global-local enrichment strategy of GFEM$��{\hspace{0.17em}}^{�\text{gl}�}�$. In such a strategy, the numerical solutions of the local problem subjected to boundary conditions derived from the global-scale problem enrich the approximation of this same global problem in an iterative procedure. Each step of the crack propagation requires a new sequence of this iterative global-local procedure. On the other hand, the constraint equation for the interface is defined only once. The crack representation in a confined region by the global-local strategy avoids a remeshing that would require new constraint equations. Two numerical problems illustrate the proposed strategy and assess the influence of the analysis parameters.

Material heterogeneity gives composite constructions unique mechanical and physical qualities. Combining multiple materials takes full use of these features in stress-constrained topology optimization. Traditional research in this field often assumes a consistent yield criterion for all possible materials but adapts their stiffness and strengths accordingly. To cope with this challenge, an innovative single-variable interpolation approach is proposed to enable the simultaneous inclusion of distinct yield criteria and material strengths. A stress-constrained topology optimization formulation is presented based on this yield function interpolation method, which can independently support various materials with different elastic characteristics, material strengths, and yield criteria. Then, the large-scale problem of local stress constraints can be effectively solved by the Augmented Lagrangian (AL) method. Several two-dimensional (2D) and three-dimensional (3D) design scenarios are investigated to reduce the overall mass of the structure while considering stress constraints. The optimal composite designs exhibit several crucial benefits resulting from material heterogeneity, including the enlargement of the design possibilities, the dispersion of stress, and the utilization of asymmetry in tension-compression strength.

This article extends recently developed finite variation sensitivity analysis (FVSA) approaches to an inverse homogenization problem. The design of metamaterials with prescribed mechanical properties is stated as a discrete density-based topology optimization problem, in which the design variables define the microstructure of the periodic base cell. The FVSA consists in estimating the finite variations of the objective and constraint functions after independently switching the state of each variable. It is used to properly linearize the functions of binary variables so the optimization problem can be solved through sequential integer linear programming. Novel sensitivity expressions were developed and it was shown that they are more accurate than the ones conventionally used in literature. Referred to as the conjugate gradient sensitivity (CGS) approach, the proposed strategy was quantitatively evaluated through numerical examples. In these examples, metamaterials with prescribed homogenized Poisson's ratios and minimal homogenized Young's moduli were obtained. A hexagonal base cell with dihedral $��{�D�}_{�3�}�$ symmetry was used to produce only metamaterials with isotropic properties. It was shown that, by using the CGS approach instead of the conventional sensitivity analysis, the sensitivity error was substantially reduced for the considered problem. The proposed developments effectively improved the stability and robustness of the discrete optimization procedures. In all the considered examples, when more accurate sensitivity analyses were performed, the parameters of the topology optimization method could be tuned more easily, yielding effective solutions even if the settings were not ideal.

This study presents a diffusive-discrete crack transition scheme for stably conducting ductile fracture simulations within a finite strain framework. In the developed scheme, the crack initiation and propagation processes are determined according to an energy minimization problem based on crack phase-field theory, and the predicted diffusive path is transformed to a discrete representation using the finite cover method during the staggered iterative scheme. In particular, for stably conducting ductile fracture simulations, three computational techniques, the staggered iterative configuration update technique, the subincremental damage update technique, and the crack opening stabilization technique, are introduced. The first and second techniques can be used regardless of whether discrete cracks are considered, and the third technique is specialized for diffusive-discrete crack transition schemes. Accordingly, ductile fracture simulations with the developed scheme rarely encounter troublesome problems such as oscillations in the displacement field and severe distortion of finite elements that can lead to divergence of calculations. After the crack phase-field model for ductile fractures is formulated and discretized, the numerical algorithms for realizing the diffusive-discrete crack transition while maintaining computational stability are explained. Several representative numerical examples are presented to demonstrate the performance and capabilities of the developed approach.

An energy-based isotropic elastoplastic damage model is developed for investigating the elastoplastic damage responses and stress–strain relationships of nano-silica incorporated concrete. The formulation employs a multiscale micromechanical framework to determine the effective elastic properties of composites at different scales. The stress–strain constitutive relation is derived by splitting the strain tensor into “elastic-damage” and “plastic-damage” parts while introducing the homogenized free potential energy function and the undamaged potential energy function. The elastoplastic damage response of the material is further characterized by elastic–plastic-damage coupling. To construct realistic 3D three-phase concrete mesostructures in numerical simulations, this paper introduces an encapsulation placement method that avoids particle overlap checking when placing aggregates. This methodology allows adjustments for the aggregate compactness as needed and enhances computational efficiency in concrete mesostructure construction. The numerical results of the modeling show good agreement with the experimental values in the open literature. Further, the influence of nano-silica addition contents and ITZ (interfacial transition zone) thicknesses on the elastoplastic damage response of nano-silica incorporated concrete are quantitatively and qualitatively investigated for the optimization of nano-silica incorporated cementitious composites. The proposed model facilitates simulating and optimizing the mechanical characteristics of nano-silica incorporated concrete and enhances the computational efficiency of 3D concrete modeling with the introduced encapsulation placement method.

A novel technique, the scaling surface-based Scaled Boundary Finite Element Method (SBFEM), is introduced as a method for formulating a general element for shell analysis. This displacement-based element includes three translational degrees of freedom (DOFs) per node. Notably, only two-dimensional discretization for one of the two parallel shell surfaces, referred to as the scaling surface, is necessary. The interpolation scheme for the scaling surface is postulated to be applicable to all surfaces parallel to it in the thickness. The derivation strictly adheres to the 3D theory of elasticity, without making additional kinematic assumptions. As a result, the displacement field along the thickness is analytically solved, and the element formulation is immune to transverse locking, membrane locking, and other issues, eliminating the need for additional remedies. Extensive investigations into the robustness and accuracy of the elements have been conducted using well-known benchmark problems, along with additional challenging problems. Numerical examples confirm that the element formulation is free from transverse shear locking and membrane locking. Moreover, the proposed formulation is easily extendable to cases involving shell elements with varying thickness and holds the potential for extension to the nonlinear response analysis of shell structures.

This article proposes a computational method for finite element analysis with deformed shape constraints for analyzing constructed structures to account for deformations that occur before shape measurement by a terrestrial laser scanner (TLS). In this method, point clouds obtained by a TLS are considered as a partial surface of the deformed structure. An analysis model is assumed to be created from CAD data or drawings. The analysis is performed under deformed shape constraints, namely, the deformed surface constraints or the normal vector constraints, which are generated by the point clouds. These constraints are introduced to reproduce the current displacements and stresses for the structure through the analysis. This method was applied to analyses of a plate and a desk using point clouds, which were created virtually on a computer or obtained by a TLS in the numerical examples. The results showed that this method can consider unexpected deformations that occur before laser scanning. Although the computed stresses oscillated when the scanned point cloud was used due to measurement errors and conventional point cloud processing methods, the stress values were responsive enough to indicate unnatural shapes of the deformed structure. Moreover, the oscillation was observed only in areas with constraints, whereas it was not seen in areas without constraints.