De-Shin Liu¹, Chin-Yi Tu¹, Cho-Liang Chung²

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.6, pp. 573-594, 2013, DOI:10.3970/cmes.2013.092.573

Abstract The Infinite Element Method (IEM) is widely used for the analysis of elastostatic structures containing singularities. In the IEM method, the problem domain is partitioned into multiple element layers, where the stiffness matrix of each layer is similar to that of the other layers in the discretized domain. However, in Mindlin-Reissner plate theory, the stiffness matrix varies through the layers of the plate, and thus the conventional IEM algorithm cannot be applied. Accordingly, the present study proposes a Plate Infinite Element Method (PIEM) in which the element stiffness matrix is separated into two sub-matrices; each being similar to the equivalent… More >

S. Brischetto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.5, pp. 367-418, 2012, DOI:10.3970/cmes.2012.088.367

Abstract The paper analyzes the hygrothermal loading effects in the bending of multilayered composite plates. Refined two-dimensional models are used to evaluate these effects, they are implemented in the framework of the Carrera's Unified Formulation (CUF) which also allows classical models to be obtained. Hygroscopic and thermal effects are evaluated by means of hygroscopic and thermal load applications, respectively. Such loads can be determined via a priori linear or constant moisture content and temperature profiles through the thickness of the plate, or by calculating them via the solution of the Fick moisture diffusion law and the Fourier heat conduction equation, respectively.… More >

M. Khezri¹, Z. Vrcelj¹, M.A. Bradford^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 271-306, 2012, DOI:10.3970/cmes.2012.087.271

Abstract A finite strip method (FSM) utilising the generalised reproducing kernel particle method (RKPM) [Behzadan, Shodja, and Khezri (2011)] is developed for the bending analysis of thin plates. In this innovative approach, the spline functions in the conventional spline finite strip method (SFSM) are replaced with generalised RKPM 1-D shape functions in the longitudinal direction, while the transverse cubic functions which are used in the conventional formulations are retained. Since the generalised RKPM is one of the class of meshfree methods which deal efficiently with derivative-type essential boundary conditions, its introduction in the FSM is beneficial for solving boundary value problems… More >

F. Tan^1,2, Y.L. Zhang¹, Y.H. Wang³, Y. Miao³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.1, pp. 1-32, 2011, DOI:10.3970/cmes.2011.075.001

Abstract The meshless hybrid boundary node method (HBNM) for solving the bending problem of the Kirchhoff thin plate is presented and discussed in the present paper. In this method, the solution is divided into two parts, i.e. the complementary solution and the particular solution. The particular solution is approximated by the radial basis function (RBF) via dual reciprocity method (DRM), while the complementary one is solved by means of HBNM. The discrete equations of HBNM are obtained from a variational principle using a modified hybrid functional, in which the independent variables are the generalized displacements and generalized tractions on the boundary… More >

Y. Suetake¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 103-110, 2006, DOI:10.3970/cmes.2006.011.103

Abstract Since Reissner and Mindlin proposed their classical thick plate theories, many authors have presented refined theories including transverse shear deformation. Most of those plate theories have tended to use higher order power series for displacements and stresses along the thickness in order to achieve the higher accuracy. However, they have not carefully noticed lateral load effect. In this paper, we pay attention to constitution of the lateral loads: a body force and upper and lower surface tractions. Especially we formulate a modified theory for plate bending, in which the effect of a body force is distinguished from that of surface… More >

Shuncai Li^1,2,3, Shichuang Zhuo⁴, Qiang Zhang⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 283-296, 2012, DOI:10.3970/cmes.2012.084.283

Abstract Based on the complex functions theory in elastic mechanics, the bending deflection formula expressed by the complex Fourier series is derived for the infinite plate with a circular opening at first, then the boundary conditions of the circular opening are expanded in Fourier Series, and the unknown coefficients of the Fourier series are determined by comparing coefficients method. By means of the convolution of the complex Fourier series and some basic formulas in the generalized functions theory, the natural boundary integral formula or the analytical deflection formulas expressed by the boundary displacement or loads are developed for the infinite plates… More >

C. R. A. Silva¹, H. P. Azikri de Deus¹, G.E. Mantovani², A.T. Beck³

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.2, pp. 119-150, 2010, DOI:10.3970/cmes.2010.067.119

Abstract In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement… More >

O.O. Oyekoya, D.U. Mba¹, A.M. El-Zafrany

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 55-86, 2008, DOI:10.3970/cmes.2008.034.055

Abstract In this paper, two new Mindlin-type plate bending elements have been derived for the modelling of functionally graded plate subjected to various loading conditions such as tensile loading, in-plane bending and out-of-plane bending. The properties of the first Mindlin-type element (i.e. Average Mindlin-type element) are computed by using an average fibre distribution technique which averages the macro-mechanical properties over each element. The properties of the second Mindlin-type element (i.e. Smooth Mindlin-type element) are computed by using a smooth fibre distribution technique, which directly uses the macro-mechanical properties at Gaussian quadrature points of each element. There were two types of non-linearity… More >

J. Sladek¹, V. Sladek¹, P. Solek², P.H. Wen³

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 57-76, 2008, DOI:10.3970/cmes.2008.028.057

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve thermal bending problems described by the Reissner-Mindlin theory. Both stationary and thermal shock loads are analyzed here. Functionally graded material properties with continuous variation in the plate thickness direction are considered here. The Laplace-transformation is used to treat the time dependence of the variables for transient problems. A weak formulation for the set of governing equations in the Reissner-Mindlin theory is transformed into local integral equations on local subdomains in the mean surface of the plate by using a unit test function. Nodal points are randomly spread on the surface… More >

Chih-Ping Wu¹, Kuan-Hao Chiu, Yun-Ming Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 163-186, 2008, DOI:10.3970/cmes.2008.027.163

Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, the Euler-Lagrange equations of three-dimensional… More >