Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 665-678, 2003, DOI:10.3970/cmes.2003.004.665

Abstract The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the various types of test functions,… More >

J. A. Nairn¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 649-664, 2003, DOI:10.3970/cmes.2003.004.649

Abstract A new algorithm is described which extends the material point method (MPM) to allow explicit cracks within the model material. Conventional MPM enforces velocity and displacement continuity through its background grid. This approach is incompatible with cracks which are displacement and velocity discontinuities. By allowing multiple velocity fields at special nodes near cracks, the new method (called CRAMP) can model cracks. The results provide an ``exact'' MPM analysis for cracks. Comparison to finite element analysis and to experiments show it gets good results for crack problems. The intersection of crack surfaces is prevented by implementing a crack contact scheme. Crack… More >

Jan Sladek¹, Vladimir Sladek¹, Chuanzeng Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 637-648, 2003, DOI:10.3970/cmes.2003.004.637

Abstract A new computational method for solving transient elastodynamic initial-boundary value problems in continuously non-homogeneous solids, based on the meshless local Petrov-Galerkin (MLPG) method, is proposed in the present paper. The moving least squares (MLS) is used for interpolation and the modified fundamental solution as the test function. The local Petrov-Galerkin method for unsymmetric weak form in such a way is transformed to the local boundary integral equations (LBIE). The analyzed domain is divided into small subdomains, in which a weak solution is assumed to exist. Nodal points are randomly spread in the analyzed domain and each one is surrounded by… More >

E. J. Sellountos¹, D. Polyzos²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 619-636, 2003, DOI:10.3970/cmes.2003.004.619

Abstract A new meshless local Petrov-Galerkin (MLPG) method for solving two dimensional frequency domain elastodynamic problems is proposed. Since the method utilizes, in its weak formulation, either the elastostatic or the frequency domain elastodynamic fundamental solution as test function, it is equivalent to the local boundary integral equation (LBIE) method. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and boundary variables is employed. Two integral equations suitable for the integral representation of the displacement fields in the local sub- domains are used. The first utilizes the… More >

Kazunori Shinohara^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.3, pp. 599-647, 2019, DOI:10.31614/cmes.2019.04472

Abstract According to the wave power rule, the second derivative of a function x(t) with respect to the variable t is equal to negative n times the function x(t) raised to the power of 2n-1. Solving the ordinary differential equations numerically results in waves appearing in the figures. The ordinary differential equation is very simple; however, waves, including the regular amplitude and period, are drawn in the figure. In this study, the function for obtaining the wave is called the leaf function. Based on the leaf function, the exact solutions for the undamped and unforced Duffing equations are presented. In the… More >

Yanxin Wang^{1, *}, Li Zhu¹, Zhi Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.2, pp. 339-350, 2019, DOI:10.31614/cmes.2019.04575

Abstract An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper. The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented. Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations. And the convergence of the Euler wavelets basis is given. The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy. More >

Lei Peng^1,2, Zhiqiang Feng^1,2,*, Pierre Joli², Christine Renaud²

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.1, pp. 111-137, 2019, DOI:10.31614/cmes.2018.04556

Abstract In order to investigate the mechanical behavior of systems with complex architecture and a large number of contacting bodies, a finite element software, named LiToTac, has been developed by using the object-oriented programming technique. This software, with an interactive graphical user interface, is able to handle highly non-linear problems including multiple contacts and large deformation. More importantly, the contact detection based on a hybrid three-stages methodology can be performed automatically, which is more efficient than the common strategies of pre-defining contact zones in commercial FEM software like ANSYS, ABAQUS, etc. In addition, the contact solver in LiToTac is portable between… More >

Yingjun Wang^1,*, Zhenpei Wang^2,*, Zhaohui Xia³, Leong Hien Poh²

CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.3, pp. 455-507, 2018, DOI:10.31614/cmes.2018.04603

Abstract Isogeometric analysis (IGA), an approach that integrates CAE into conventional CAD design tools, has been used in structural optimization for 10 years, with plenty of excellent research results. This paper provides a comprehensive review on isogeometric shape and topology optimization, with a brief coverage of size optimization. For isogeometric shape optimization, attention is focused on the parametrization methods, mesh updating schemes and shape sensitivity analyses. Some interesting observations, e.g. the popularity of using direct (differential) method for shape sensitivity analysis and the possibility of developing a large scale, seamlessly integrated analysis-design platform, are discussed in the framework of isogeometric shape… More >

Adrien Scheuer^{1, 3, *}, Amine Ammar², Emmanuelle Abisset-Chavanne³, Elias Cueto⁴, Francisco Chinesta⁵, Roland Keunings¹, Suresh G. Advani⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.3, pp. 367-386, 2018, DOI:10.31614/cmes.2018.04278

Abstract Describing the orientation state of the particles is often critical in fibre suspen-sion applications. Macroscopic descriptors, the so-called second-order orientation tensor (or moment) leading the way, are often preferred due to their low computational cost. Clo-sure problems however arise when evolution equations for the moments are derived from the orientation distribution functions and the impact of the chosen closure is often unpre-dictable. In this work, our aim is to provide macroscopic simulations of orientation that are cheap, accurate and closure-free. To this end, we propose an innovative data-based approach to the upscaling of orientation kinematics in the context of fibre… More >

Yang Yang^1,*, Jinbao Duan¹, Haitao Yu¹, Zhipeng Gao¹, Xuesong Qiu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.3, pp. 555-575, 2018, DOI:10.31614/cmes.2018.04249

Abstract The development of deep learning has revolutionized image recognition technology. How to design faster and more accurate image classification algorithms has become our research interests. In this paper, we propose a new algorithm called stochastic depth networks with deep energy model (SADIE), and the model improves stochastic depth neural network with deep energy model to provide attributes of images and analysis their characteristics. First, the Bernoulli distribution probability is used to select the current layer of the neural network to prevent gradient dispersion during training. Then in the backpropagation process, the energy function is designed to optimize the target loss… More >