Mohd. Ahmed^1,*, Mohamed Hechmi El Ouni¹, Devinder Singh², Nabil Ben Kahla¹

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.2, pp. 687-786, 2019, DOI:10.32604/cmes.2019.06886

Abstract The paper presents a parametric study on interpolation techniques based postprocessed error estimation in finite element elastic analysis by varying important parameters of recovery, interpolation scheme and type of patch construction. The quality of error estimation with recovery parameters is compared in terms of local and global effectivity of error estimation, rate of error convergence, and adaptively refined meshes. A mesh free moving least square interpolation technique with proven reliability and effectivity is introduced for improving the recovery of finite element solution errors. The post-processed finite element solutions of elastic problems are presented for performance study under different parameters of… More >

H. Theilig¹

Structural Durability & Health Monitoring, Vol.6, No.3&4, pp. 239-272, 2010, DOI:10.3970/sdhm.2010.006.239

Abstract The aim of this paper is to give an overview to some problems and solutions of the fracture analysis of 2D structures. It will be shown that the common computer-aided two-dimensional fatigue crack path simulation can be considerably improved in accuracy by using a predictor-corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method. Furthermore the paper presents an improved finite element technique for the calculation of stress intensity factors of mixed mode problems by the MVCCI Method. The procedure is devised to compute the separated strain energy release rates by using the convergence of two separate… More >

Xiuqing Qian^1,2, Fan yuan^1,*

Molecular & Cellular Biomechanics, Vol.16, Suppl.2, pp. 89-89, 2019, DOI:10.32604/mcb.2019.07041

Abstract Elevated intraocular pressure (IOP) is the most important risk factor for disease progression in glaucoma patients. The elevation is predominantly due to the increase in the aqueous outflow resistance in the trabecular outflow pathway. Recent data have shown that the resistance increase is correlated with changes in the tissue stiffness. To this end, we developed a mathematical model to simulate how the tissue stiffness can affect the deformation of the trabecular meshwork (TM) that can be determined experimentally. The goal of the study is to develop a method to non-invasively determine the TM stiffness in patients through measurement of the… More >

P.H. Wen¹, M.H. Aliabadi²

Structural Durability & Health Monitoring, Vol.8, No.3, pp. 223-248, 2012, DOI:10.32604/sdhm.2012.008.223

Abstract A mesh-free method for modelling crack growth in functionally graded materials is presented. Based on the variational principle of the potential energy, mesh-free method has been implemented with enriched radial bases interpolation functions to evaluate mixed-mode stress intensity factors, which are introduced to capture the singularity of stress at the crack tip. Paris law and the maximum principle stress criterion are adopted for defining the growth rate and direction of the fatigue crack growth respectively. The accuracy of the proposed method is assessed by comparison to other available solutions. More >

P.H. Wen¹, M.H. Aliabadi²

Structural Durability & Health Monitoring, Vol.3, No.2, pp. 107-120, 2007, DOI:10.3970/sdhm.2007.003.107

Abstract In the last decade, meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. Based on the variation of potential energy, the element-free Galerkin method is developed on the basis of finite element method by the use of radial basis function interpolation. An enriched radial basis function is formulated to capture the stress singularity at the crack tip. The usual advantages of finite element method are retained in this method but now significant improvement of accuracy. Neither the connectivity of mesh in the domain by the finite element method or integrations… More >

L.S. Miers¹, J.C.F. Telles²

Structural Durability & Health Monitoring, Vol.1, No.3, pp. 225-232, 2005, DOI:10.3970/sdhm.2005.001.225

Abstract The present paper aims at introducing the concept of Green's function type fundamental solutions (i.e., unit source fundamental solutions satisfying particular boundary conditions) into the context of meshless approaches, particularly dealing with the local boundary integral equation method (LBIE) derived from the classic boundary integral equation procedure. The Green's functions discussed here are mainly the so-called half-plane solution, corresponding to a unit source within a semi-plane bounded by a flux-free straight line and an infinite plane containing internal lines of potential discontinuity. The latter is here introduced in numerical fashion, as an extension of the authors' previous numerical Green's function… More >

J. Sladek¹, V. Sladek, Ch.Zhang²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 131-144, 2005, DOI:10.3970/sdhm.2005.001.131

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-d), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static and transient elastodynamic problems are considered. For time-dependent problems, the Laplace-transform technique is utilized. A unit step function is used as the test function in the local weak-form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The analyzed domain is divided into small subdomains with a circular shape. The moving least-squares (MLS) method is adopted for approximating the physical… More >

G. Dhondt¹

Structural Durability & Health Monitoring, Vol.1, No.1, pp. 21-34, 2005, DOI:10.3970/sdhm.2005.001.021

Abstract An algorithm is described which allows for the automatic calculation of crack propagation due to cyclic loading under mixed-mode conditions. The core of the procedure deals with the insertion of an arbitrarily formed crack into a virgin 20-node brick element mesh, thereby generating new quadratic bricks. One especially difficult aspect is the extension of the triangulation of the crack surface up to the boundary of the crack front elements. In the present article the technique is applied to linear elastic calculations using the stress intensity factor concept and a Paris-type law. However, other crack propagation parameters and crack propagation laws… More >

S. G. Bardenhagen^1,2, E. M. Kober³

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 477-496, 2004, DOI:10.3970/cmes.2004.005.477

Abstract The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov–Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point(GIMP) methods. The generalizationpermits identification with aspects of other point or node based discrete solution techniques which do not use a body–fixed grid, i.e. the “meshless methods”. Similarities are noted and some practical advantages relative to some of these methods are identified. Examples are used to demonstrate and explain numerical artifact noise which can be expected inMPM calculations. Thisnoiseresultsin non-physical local variations at the material points,… More >

G. C. Bourantas¹, E. D. Skouras^2,3, V. C. Loukopoulos⁴, G. C. Nikiforidis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.2, pp. 187-212, 2010, DOI:10.3970/cmes.2010.064.187

Abstract Meshfree point collocation method (MPCM) is developed, solving the velocity-vorticity formulation of Navier-Stokes equations, for two-dimensional, steady state incompressible viscous flow problems in the presence of heat transfer. Particular emphasis is placed on the application of the velocity-correction method, ensuring the continuity equation. The Gaussian Radial Basis Functions (GRBF) interpolation is employed to construct the shape functions in conjunction with the framework of the point collocation method. The cases of forced, natural and mixed convection in a 2D rectangular enclosure are examined. The accuracy and the stability of the proposed scheme are demonstrated through three representative, well known and established… More >