International Journal for Numerical Methods in Engineering

doi: 10.1002/nme.6223pmid: N/A

Magisano, D. ; Garcea, G.

doi: 10.1002/nme.6380pmid: N/A

This work presents an efficient fiber analysis for evaluating the shakedown safety factor of three‐dimensional frames under multiple load combinations. Mixed finite elements are employed for an accurate discretization. A continuation method, similar to a standard elasto‐plastic analysis, is used at structural level. It evaluates a pseudo‐equilibrium path made of a sequence of safe states with a converging nondecreasing load factor. Each point of the path is obtained by finding kinematic variables corresponding to self‐equilibrated stresses satisfying Melan's condition for the current load factor to be safe. The stress admissible domain is defined at fiber level as a function of the load factor using the maximum and minimum effect due to all loads. An iterative state determination provides finite element stresses corresponding to assigned kinematic variables and load factor. The overall analysis differs from previous proposals for two novelty points. Firstly, a direct application of the Newton method can be employed, without any need for constrained optimization solvers. Moreover, dimension and complexity of the load domain do not affect the computational cost of the nonlinear analysis. Numerical tests show an accurate estimate of the safety factor using a small number of fibers and an efficient solution also for large buildings.

Zhang, Kun ; Shen, Shui‐Long; Zhou, Annan

doi: 10.1002/nme.6381pmid: N/A

This article proposes an approach to resolve the dynamic fracture of brittle materials by incorporating eigenerosion into the material point method (MPM) framework. The eigenerosion approach links the crack propagation to energy conservation based on the variational theory of fracture mechanics. This idea closely resembles the conventional treatment for the phase‐field method. The major difference is that the effective energy release rate of each particle that controls the crack propagation is only calculated within its neighborhood domain for the eigenerosion approach. Because evaluation of the material's fracture behavior can be decoupled from the governing equations as a separate solution step, the eigenerosion scheme allows straightforward implementation into any standard MPM solver with minor modifications. In addition, a phantom‐node method is employed to handle the preexisting crack. With these settings, the proposed model can capture complex fracture behaviors. Several representative benchmark tests demonstrate the efficiency and validity of the proposed model.

Kulikov, G. M. ; Plotnikova, S. V.; Glebov, A. O.

doi: 10.1002/nme.6382pmid: N/A

In this work, the finite rotation exact geometry four‐node solid‐shell element using the sampling surfaces (SaS) method is developed for the analysis of the second Piola‐Kirchhoff stresses in laminated piezoelectric shells. The SaS method is based on choosing inside the layers the arbitrary number of SaS parallel to the middle surface and located at Chebyshev polynomial nodes in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The outer surfaces and interfaces are also included into a set of SaS. To circumvent shear and membrane locking, the hybrid‐mixed solid‐shell element on the basis of the Hu‐Washizu variational principle is proposed. The tangent stiffness matrix is evaluated by 3D analytical integration throughout the finite element. This novelty provides a superior performance in the case of coarse meshes. A comparison with the SOLID226 element showed that the developed exact geometry SaS solid‐shell element allows the use of load increments, which are much larger than possible with existing displacement‐based finite elements. Thus, it can be recommended for the 3D stress analysis of doubly‐curved laminated piezoelectric shells because the SaS formulation gives the opportunity to obtain the 3D solutions of electroelasticity with a prescribed accuracy.

Sanfui, Subhajit; Sharma, Deepak

doi: 10.1002/nme.6383pmid: N/A

With the development of parallel computing architectures, larger and more complex finite element analyses (FEA) are being performed with higher accuracy and smaller execution times. Graphics processing units (GPUs) are one of the major contributors of this computational breakthrough. This work presents a three‐stage GPU‐based FEA matrix generation strategy with the key idea of decoupling the computation of global matrix indices and values by use of a novel data structure referred to as the neighbor matrix. The first stage computes the neighbor matrix on the GPU based on the unstructured mesh. Using this neighbor matrix, the indices and values of the global matrix are computed separately in the second and third stages. The neighbor matrix is computed for three different element types. Two versions for performing numerical integration and assembly in the same or separate kernels are implemented and simulations are run for different mesh sizes having up to three million degrees of freedom on a single GPU. Comparison with GPU‐based parallel implementation from the literature reveals speedup ranging from 4× to 6× for the proposed workload division strategy. Furthermore, the same kernel implementation is found to outperform the separate kernel implementation by 70% to 150% for different element types.

Badías, Alberto ; González, David; Alfaro, Icíar; Chinesta, Francisco; Cueto, Elías

doi: 10.1002/nme.6385pmid: N/A

We present a real‐time method for computing the mechanical interaction between real and virtual objects in an augmented reality environment. Using model order reduction methods we are able to estimate the physical behavior of deformable objects in real time, with the precision of a high‐fidelity solver but working at the speed of a video sequence. We merge tools of machine learning, computer vision, and computer graphics in a single application to describe the behavior of deformable virtual objects allowing the user to interact with them in a natural way. Three examples are provided to test the performance of the method.

Mendonça, Tiago S.; Peixoto, Rodrigo G.; Ribeiro, Gabriel O.

doi: 10.1002/nme.6387pmid: N/A

Material failure analysis are addressed by the continuum strong discontinuity approach within the implicit formulation of the boundary element method in this work. An automatic cell generation algorithm is used to track cracks during the loading processes in the nonlinear analysis. As a major novelty, a new class of cells with embedded discontinuity is developed in which nonuniform displacement jump components are considered. It is shown that this new approach eliminates the stress locking effect verified in propagation analyses using cells with embedded uniform discontinuous displacement field, since the relative rotational motion between the two portions of a cell can now be properly captured.

Wang, Jingbo ; Faltinsen, Odd Magnus; Duan, Wenyang

doi: 10.1002/nme.6390pmid: N/A

A high‐order harmonic polynomial method (HPM) is developed for solving the Laplace equation with complex boundaries. The “irregular cell” is proposed for the accurate discretization of the Laplace equation, where it is difficult to construct a high‐quality stencil. An advanced discretization scheme is also developed for the accurate evaluation of the normal derivative of potential functions on complex boundaries. Thanks to the irregular cell and the discretization scheme for the normal derivative of the potential functions, the present method can avoid the drawback of distorted stencils, that is, the possible numerical inaccuracy/instability. Furthermore, it can involve stationary or moving bodies on the Cartesian grid in an accurate and simple way. With the proper free‐surface tracking methods, the HPM has been successfully applied to the accurate and stable modeling of highly nonlinear free‐surface potential flows with and without moving bodies, that is, sloshing, water entry, and plunging breaker.

Sato, Yuki; Izui, Kazuhiro; Yamada, Takayuki; Nishiwaki, Shinji

doi: 10.1002/nme.6393pmid: N/A

This article presents a robust topology optimization method for optical cloaks under uncertainties in the wave number and angle in the incident wave. We first discuss the governing equation derived from Maxwell's equation, and extend it to the entire domain including the dielectric material and air, based on the level set‐based topology optimization method. Next, a robust optimization problem is formulated as a minimization problem of the weighted sum of the scattered wave norm and its standard deviation with respect to the wave number and angle of the incident wave. The standard deviation is mathematically expressed by the Taylor series approximation and the use of the adjoint variable method. The design sensitivity of the objective functional is also derived by the adjoint variable method. An optimization algorithm is then constructed, based on the proposed formulation for robust designs of optical cloaks. Several numerical examples are finally provided to demonstrate the validity and utility of the proposed method.

Li, Jian; Yin, Zhen‐Yu

doi: 10.1002/nme.6394pmid: N/A

Integration of stress‐strain‐time relationship is a key issue for the application of elasto‐viscoplastic models to engineering practice. This article presents a novel adaptive substepping cutting‐plane time integration scheme for elasto‐viscoplastic models keeping the advantage of original cutting‐plane (OCP) with only the first derivatives of loading surface required. The deficiency of OCP time integration algorithm is first discussed taking a simple overstress theory based elasto‐viscoplastic modified Cam‐Clay model (EVP‐MCC) as example. To overcome this, a new algorithm is developed with three features: (1) an evolution function for the hardening variable of dynamic loading surface is innovatively deduced for the Taylor series approximation, (2) the elastic predictor is modified to account for the initial viscoplastic strain rate with more accuracy, and (3) a new adaptive substepping technique for restricting simultaneously both strain and time incremental sizes based on the overstress distance is proposed. For easy understanding, the proposed algorithm is first presented for one‐dimensional condition, and then extended to three‐dimensional condition. The new integrated EVP‐MCC model using the proposed algorithm is examined by simulating laboratory tests at both levels of integration point and finite element with a good performance in terms of accuracy and convergence.