Ping Hu¹, Yang Xia¹, Limin Tang²

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 103-136, 2011, DOI:10.3970/cmes.2011.073.103

Abstract In this paper, an assumed displacement quasi-conforming finite element method with truncated polynomial expansions of in-domain displacements and derived expansions of strains is introduced. Based on the method a four-node quadrilateral flat shell element with complete quadratic polynomials for membrane and bending displacement fields is developed. Numerical tests are carried out for validation of the present element. The results show that the present element preserves all the advantages of the quasi-conforming i.e., explicit stiffness matrix, convenient post processing and free from membrane locking and shear locking. The tests also prove that the present element gives excellent results, especially for the… More >

H. T. Wang^1,2, Z. H. Yao³

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.2, pp. 115-148, 2011, DOI:10.3970/cmes.2011.072.115

Abstract A fast boundary element solver for the analysis of three-dimensional general crack problems is presented. In order to effectively model the embedded or edge cracked structures a dual boundary integral equation (BIE) formulation is used. By implementing the fast multipole method (FMM) to the discretized BIE, structures containing a large number of three-dimensional cracks can be readily simulated on one personal computer. In the FMM framework, a multipole expansion formulation is derived for the hyper-singular integral in order that the multipole moments of the dual BIEs containing the weakly-, strongly- and hyper-singular kernels are collected and translated with a unified… More >

E. Carrera, S. Brischetto¹, M. Cinefra²

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.3, pp. 259-342, 2010, DOI:10.3970/cmes.2010.065.259

Abstract This paper investigates the problem of free vibrations of multilayered plates and shells embedding anisotropic and thickness polarized piezoelectric layers. Carrera's Unified Formulation (CUF) has been employed to implement a large variety of electro-mechanical plate/shell theories. So-called Equivalent Single Layer and Layer Wise variable descriptions are employed for mechanical and electrical variables;linear to fourth order expansions are used in the thickness direction z in terms of power of z or Legendre polynomials. Various forms are considered for the Principle of Virtual Displacements (PVD) and Reissner's Mixed Variational Theorem (RMVT) to derive consistent differential electro-mechanical governing equations. The effect of electro-mechanical… More >

S. Ullah¹, B. Pichler¹, S. Scheiner^1,2, C. Hellmich^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.3, pp. 279-316, 2010, DOI:10.3970/cmes.2010.057.279

Abstract Point-wise optical measurements of 3D displacement vectors over time are a key input for monitoring shotcrete tunnel shells during construction according to the New Austrian Tunnelling Method (NATM). Aiming at estimation of the stresses prevailing in the highly loaded, hydrating material, we here deal with two different interpolation strategies for reconstructing, from measured displacement vectors, the 3D displacement field histories of the inner surface of the tunnel shell. The first approach considers spatial interpolation of displacement components in a fixed Cartesian base frame, while the second (new) approach refers to displacement components in a moving base frame consisting of vectors… More >

C. Y. Chen¹, C. Atkinson²

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.3, pp. 219-240, 2009, DOI:10.3970/cmes.2009.048.219

Abstract In this paper, we extend our previous analysis of a contact problem with a circular indenter pressed normally against a semi-infinite elastic composite to that of a semi-infinite viscoelastic composite which consists of a contact layer with uniform thickness welded together with another dissimilar medium. Using the correspondence principle between the Laplace transformed elastic equations and the viscoelastic ones, the asymptotic results derived previously for the pure elastic case are readily adopted for the viscoelastic one with the elastic constants replaced by appropriate functions of Laplace transformed variables for the linear viscoelastic solid. We focus our analysis on the force… More >

S Reaz Ahmed¹, S K Deb Nath¹

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 35-64, 2009, DOI:10.3970/cmes.2009.044.035

Abstract The paper presents a simplified analysis of stresses and deformations at critical sections of a tire-tread. Displacement potential formulation is used in conjunction with the finite-difference method to model the present contact problem. The solution of the problem is obtained for two limiting cases of the contact boundary - one allows the lateral slippage and the other conforms to the no-slip condition along the lateral direction. The influential effects of tire material and tread aspect-ratio are discussed. The reliability and accuracy of the solution is also discussed in light of comparison made with the usual computational approach. More >

V.V. Zozulya¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.3, pp. 187-216, 2009, DOI:10.3970/cmes.2009.042.187

Abstract The mathematical statement for contact problem with unilateral restrictions and friction is done in classical and weak forms. Different variational formulation of unilateral contact problems with friction based on principles of virtual displacements and virtual stresses are considered. Especially boundary variational functionals that are used with boundary integral equations have been established. Nonsmooth optimization algorithms of Udzawa type for solution of unilateral contact problem with friction have been developed. Some theoretical results of existence and uniqueness in elastostatic unilateral contact problem with friction are outlined. More >

G. M. Kulikov¹, S. V. Plotnikova¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 15-38, 2008, DOI:10.3970/cmes.2008.028.015

Abstract This paper presents a robust non-linear geometrically exact four-node solid-shell element based on the first-order seven-parameter equivalent single-layer theory, which permits us to utilize the 3D constitutive equations. The term "geometrically exact" reflects the fact that geometry of the reference surface is described by analytically given functions and displacement vectors are resolved in the reference surface frame. As fundamental shell unknowns six displacements of the outer surfaces and a transverse displacement of the midsurface are chosen. Such choice of displacements gives the possibility to derive strain-displacement relationships, which are invariant under arbitrarily large rigid-body shell motions in a convected curvilinear… More >

Shunde Yin¹, Leo Rothenburg¹, Maurice B. Dusseault¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 111-120, 2007, DOI:10.3970/cmes.2007.019.111

Abstract Subsidence problem is of great importance in petroleum engineering and environmental engineering. In this paper, we firstly apply a hybrid Displacement Discontinuity-FEM modeling to this classic problem: the evaluation of subsidence over a compacting oil reservoir. We use displacement discontinuity method to account for the reservoir surrounding area, and finite element methods in the fully coupled simulation of the reservoir itself. This approach greatly reduces the number of degrees of freedom compared to an analyzing fully coupled problem using only a finite element or finite difference discretization. More >

S. N. Atluri¹, Z. D. Han¹, S. Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 507-518, 2003, DOI:10.3970/cmes.2003.004.507

Abstract The general Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement & traction boundary integral equations are presented, for solids undergoing small deformations. These 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, in the MLPG-type weak-forms of the non-hyper-singular dBIE and tBIE over the local sub-boundary surfaces, several types of MLPG/BIEs are formulated, while also… More >