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… 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… More >

Humihiko Gotou¹, Takashi Kuwataka¹, Terumasa Nishihara¹, Tetsuo Iwakuma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 319-328, 2003, DOI:10.3970/cmes.2003.004.319

Abstract The stiffness equation in finite displacement problems is often derived from the virtual work equation, partly in order to avoid the complicated formulation based on the potential functional. Describing the virtual rotational angles by infinitesimal rotational angles about three axes of the right-angled Cartesian coordinate system, we formulate tangent stiffness equations whose rotational degrees of freedom are described by rotational angles about the three axes. The rotational degrees of freedom are useful to treat three rotational components in nodal displacement vectors as vector components for coordinate transformation, when non-vector components like Euler's angles are used More >

S. Okamoto¹, Y. Omura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 287-300, 2003, DOI:10.3970/cmes.2003.004.287

Abstract The purpose of this study is to develop a procedure for performing a dynamic analysis in the case that a structure undergoes large translational and rotational displacements when moving along a nonlinear trajectory at variable velocity. Finite-element equations of motion that include the inertial force of the structure's motion have been derived. The equations also account for the geometric nonlinearity that has to be considered in a problem of finite translational and rotational displacements. A finite rotational matrix was used to transfer vectors or matrices measured in a certain coordinate frame to those measured in More >

K. Ijima¹, H. Obiya¹, S. Iguchi², S. Goto²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 239-248, 2003, DOI:10.3970/cmes.2003.004.239

Abstract Defining element coordinates in space frame, element end deformations become statically clear from the energy principle. Therefore, the deformations can be expressed by nodal displacement without any approximation. The paper indicates that the exact expressions of the deformations and the geometrical stiffness strictly based on the equations makes large displacement analysis of space frame possible with robustness on the computation. More >

Z.Tang, S. Shen, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 177-196, 2003, DOI:10.3970/cmes.2003.004.177

Abstract A meshless numerical implementation is reported of the 2-D Fleck-Hutchinson phenomenological strain-gradient theory, which fits within the framework of the Toupin-Mindlin theories and deals with first-order strain gradients and the associated work-conjugate higher-order stresses. From a mathematical point of view, the two-dimensional Toupin-Mindlin strain gradient theory is a generalization of the Poisson-Kirchhoff plate theories, involving, in addition to the fourth-order derivatives of the displacements, also a second-order derivative. In the conventional displacement-based approaches in FEM, the interpolation of displacement requires C$^{1}$ --continuity (in order to ensure convergence of the finite element procedure for 4$^{th}$ order… More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 5-20, 2003, DOI:10.3970/cmes.2003.004.005

Abstract Using the directly derived non-hyper singular integral equations for displacement gradients [as in Okada, Rajiyah, and Atluri (1989a)], simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are presented. A large number of ``intrinsic properties'' of the fundamental solutions in elasticity are developed, and are used in rendering the tBIE and dBIE to be only weakly-singular, in a very simple manner. The solutions of the weakly singular tBIE and dBIE through either global Petrov-Galerkin type ``boundary element methods'', or, alternatively, through the meshless local Petrov-Galerkin (MLPG) methods, are discussed. As More >

Shuangbiao Liu, Michael J. Rodgers, Qian Wang, Leon M. Keer, Herbert S. Cheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.4, pp. 465-482, 2002, DOI:10.3970/cmes.2002.003.465

Abstract Computing the temperature rise and thermoelastic displacement of a material subjected to frictional heating is essential for the realistic modeling of the performance of mechanical components. This paper presents a novel set of frequency-domain expressions for the surface temperature rise and the surface normal thermoelastic displacement of a moving three-dimensional elastic halfspace subjected to arbitrary transient frictional heating, where the velocity of the body and its direction can be an arbitrary function of time. Frequency response functions are derived by using the Carslaw-Jaeger theory, the Seo-Mura result, and the Fourier transform. General formulas are expressed More >

Ru-Min Chao, Yen-Ji Chen, F.C. Lin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 73-86, 2001, DOI:10.3970/cmes.2001.002.073

Abstract The two-dimensional elasticity problem of an isotropic material, containing a centered-crack with unknown boundary traction is studied by the inverse procedure. The dual boundary integral equations are used to analyze the problem. While solving the ill-posed inverse problem, both of the conjugate gradient method and the regularization method are used. A scaling factor depending upon the material constant μ is introduced into the sensitivity matrix in order to keep the order of magnitude the same throughout the formulation. The result by using the displacement measurement will be compared with those by stress measurement, and an extensive More >