E. Tonti, F. Zarantonello¹

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 37-70, 2010, DOI:10.3970/cmes.2010.064.037

Abstract This paper completes a preceeding paper on the algebraic formulation of elastostatics [Tonti, Zarantonello (2009)]. It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of differential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual subdivision of the time axis, as we did for a space cell complex. The mass matrix obtained with the direct algebraic formulation is diagonal. More >

Mira Mitra¹, S. Gopalakrishnan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.1, pp. 49-68, 2006, DOI:10.3970/cmes.2006.015.049

Abstract In this paper, a 2-D Wavelet based Spectral Finite Element (WSFE) is developed and is used to study wave propagation in an isotropic plate. Here, first, wavelet approximation is done in both temporal and one spatial (lateral) dimension to reduce the governing partial differential wave equations to a set of Ordinary Differential Equations (ODEs). Daubechies compactly supported orthogonal scaling functions are used as basis which allows finite domain analysis and easy imposition of initial/boundary conditions. However, the assignment of initial and boundary conditions in time and space respectively, are done following two different methods. Next, the reduced ODEs are solved… More >

Souli Mhamed¹, Paul Du Bois², Essam Al-Bahkali^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.1, pp. 91-107, 2018, DOI:10.31614/cmes.2018.03888

Abstract When the simulation takes account of dissipative mechanisms, e.g. heat conduction and viscosity, the shocks become smeared out to produce thin layers of rapidly and continuously varying energy, density, pressure and velocity rather than discrete surfaces of mathematical discontinuity. In the mid twentieth century, Von Neumann and Richtmyer suggested the use of a viscous pressure term (bulk viscosity) in the equilibrium equations for ideal gases in order to examine the shock while avoiding numerical oscillations at the shock front. When the bulk viscosity is included in the conservation equations, the comprehensive physics present a continuous solution satisfying the Rankine-Hugoniot conditions.… More >

Dongdong Wang, Zhuoya Li, Youcai Wu

The International Conference on Computational & Experimental Engineering and Sciences, Vol.17, No.4, pp. 107-108, 2011, DOI:10.3970/icces.2011.017.107

Abstract Meshfree methods have experienced substantially fundamental development and various applications. One distinguished advantage for meshfree methods is that they can relieve the mesh tangling burden of FEM and are more suitable for finite deformation analysis. In this work a three dimensional updated Lagrangian Galerkin meshfree formulation with improved computational efficiency is presented to analyze the failure of soil slopes. This nonlinear meshfree formulation is featured by the Lagrangian stabilized conforming nodal integration method where the low cost nature of nodal integration approach is kept and at the same time the numerical stability is obtained as is not the case for… More >

H.B. Chen

The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.4, pp. 105-106, 2011, DOI:10.3970/icces.2011.020.105

Abstract The calculation of field values and their derivatives near the domain boundary through the boundary element method (BEM) will meet the nearly singularity problem, i.e. the boundary layer effect problem. The tangential derivatives of field values on the boundary often meet an obvious deduction of calculation accuracy. An effective algorithm was proposed by Chen et al. [1,2] to treat these two problems in the same time in elastic BEM and it was recently extended to calculate the second derivative values in potential problem [3]. This algorithm is based on the regularized formulations and is now called the regularized indirect algorithm.… More >

Jun Wang, David CC LAM

The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.3, pp. 89-90, 2011, DOI:10.3970/icces.2011.020.089

Abstract Selected elastic and plastic behaviors of materials have been shown to exhibit size-dependence when they are in the micro-nanoscale. Experiments have shown that the scale-dependent behavior can be modeled by adding strain gradient terms into the finite element models, but modifications need to satisfy C1 displacement continuity in the models. In this investigation, meshless finite element formulation, where C1 continuity can be satisfied without new additions nodal degrees of freedom, was developed. In the formulation, the strain gradients were decomposed into dilatation, stretch and rotation parts; and the governing equations were discretized on local domains using the meshless local Petrov-Galekin… More >

Wojciech Pietraszkiewicz

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.3, pp. 89-90, 2011, DOI:10.3970/icces.2011.016.089

Abstract Wei-zhang Chien (1944) derived the equilibrium equations and the compatibility conditions of the nonlinear theory of thin, isotropic elastic shells entirely in terms of the surface stress and strain measures associated with the shell base surface. This allowed Him to divide the complex boundary value problem (BVP) of nonlinear shell analysis into two disjoint and supposedly simpler steps: I) finding the surface stress and strain measures, and II) establishing displacements from already known surfacestrainmeasures. In the present paper some achievements of this formulation obtained during the last 66 years are reviewed, with special account of the results obtained by the… More >

Ney Augusto Dumont

The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 192-192, 2019, DOI:10.32604/icces.2019.05284

Abstract The use of boundary integral equations as an attempt to solve general problems of elasticity and potential has largely preceded the use of domain-related developments, which only became feasible (and conceivable) with the advent of powerful computational devices. On the other hand, the present-day matrix, computational-ready outline of the boundary element method (including its nowadays prevalent name) has borrowed – in part correctly and in part wrongly – much from the finite element concepts and formulation. We propose a revisit of the method, including, as for elasticity problems: a) conceptual reformulation in terms of weighted residuals with a consistent derivation… More >

G. R. Liu^{1, 2}

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.4, pp. 113-114, 2009, DOI:10.3970/icces.2009.012.113

Abstract This paper introduces first a weakened weakform (W2) using a generalized gradient smoothing technique for an unified formulation of a wide class of compatible and incompatible displacement methods including settings of the finite element methods (FEM) and meshfree methods of special properties including the upper bound properties. A G space is first defined to include discontinuous functions allowing the use of much more types of methods/techniques to create shape functions for numerical models; Properties and a set of important inequalities for G spaces are then proven in theory and analyzed in detail. We prove that the numerical methods developed based… More >

T. Asada¹, N. Ohno¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.4, No.4, pp. 201-206, 2007, DOI:10.3970/icces.2007.004.201

Abstract In this study, to determine incremental, perturbed displacement fields in periodic inelastic solids, an incremental homogenization problem is fully implicitly formulated, and an algorithm is developed to solve the homogenization problem. It is shown that the homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increments in unit cells, and that the present formulation allows versatility in the initial setting of strain increments in contrast to previous studies. The homogenization algorithm developed is then examined by analyzing a holed plate, with an elastoplastic micro-structure, subjected to tensile loading. It is thus demonstrated that the convergence in… More >