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 >

Arif Amirov¹, Fikret Gölgeleyen¹, Ayten Rahmanova²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.4, pp. 125-136, 2009, DOI:10.3970/icces.2009.012.125

Abstract This paper has two purposes. The first is to prove the existence and uniqueness of the solution of an inverse problem for the general linear kinetic equation with a scattering term. The second one is to develop a numerical approximation method for the solution of this inverse problem for two dimensional case using finite difference method. 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 >

F. Cosmi¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 195-210, 2007, DOI:10.3970/icces.2007.003.195

Abstract The Cell Method is a recently developed numerical method that is giving interesting results in several fields of physics and engineering. In this paper, first a brief description of the method for elasticity problems is given and successively the elastodynamics formulation is derived. The method leads to an explicit solution system, combining the advantages of a diagonal mass matrix and the possibility of using unstructured meshes. The convergence rate has been tested in reference to the problem of free harmonic vibrations in a system with one degree of freedom, showing that the Cell Method has the same convergence rate of… More >

S.S. Chen¹, Y.H. Liu¹, Z.Z. Cen¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.3, pp. 145-150, 2007, DOI:10.3970/icces.2007.003.145

Abstract A solution procedure for lower bound limit analysis is presented making use of the element free Galerkin (EFG) method rather than of the traditional numerical methods such as finite element method and boundary element method. A reduced basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. Numerical example in this paper shows that it is feasible and efficient to solve the problems of limit analysis by using the EFG method. More >

M-A Lavoie¹, A. Gakwaya¹, M. Nejad Ensan², D.G. Zimcik²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.2, No.4, pp. 111-118, 2007, DOI:10.3970/icces.2007.002.111

Abstract This paper reviews numerical methods that are currently available to simulate bird strike as well as the theory of the event. It also summarizes important parameters and provides guidelines as to how to set up the analysis and how to evaluate a model. The information provided is based on physical properties and available results regarding a bird and its behaviour upon impact. The simulations have been performed with LS-DYNA 970 but can be done in similar dynamic finite elements analysis codes. More >

S.C. Forth¹, A. Staroselsky²

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.3, pp. 287-298, 2005, DOI:10.3970/cmes.2005.009.287

Abstract A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating, and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack and external surface. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus, when modeling crack growth, the finite… More >

F. Cosmi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 191-200, 2005, DOI:10.3970/cmes.2005.008.191

Abstract The Cell Method is a recently developed numerical method that is giving interesting results in several fields of physics and engineering. In this paper, first a brief description of the method for elasticity problems is given and successively the elastodynamics formulation is derived. The method leads to an explicit solution system, combining the advantages of a diagonal mass matrix and the possibility of using unstructured meshes. The convergence rate has been tested in reference to the problem of free harmonic vibrations in a system with one degree of freedom, showing that the Cell Method has the same convergence rate of… More >

Benjamin Castaneda^∗, Juvenal Ormachea^†, Paul Rodríguez^‡, Kevin J. Parker^§

Molecular & Cellular Biomechanics, Vol.10, No.1, pp. 43-65, 2013, DOI:10.3970/mcb.2013.010.043

Abstract Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of… More >

H. T. Xiao^1,2,3, Y. Y. Xie^1,2, Z. Q. Yue⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.1, pp. 55-80, 2015, DOI:10.3970/cmes.2015.109.055

Abstract This paper examines the problem of a square-shaped crack embedded in a layered half-space whose external surface is subject to a uniform loading over a rectangular area. Two novel numerical methods and the superposition principle in fracture mechanics are employed for the analysis of the crack problem. The numerical methods are based on the fundamental solution of a multilayered elastic medium and are, respectively, applied to calculate the stress fields of layered halfspace without cracks and the discontinuous displacements of crack surfaces in layered halfspace. The stress intensity factor (SIF) values are calculated using discontinuous displacements and the influence of… More >