مقاله Three dimensional static and dynamic analysis of thick functionally graded plates by the meshless local Petrov

خلاصه مقاله

In this paper, three dimensional (3D) static and dynamic analysis of thick functionally graded plates based on the Meshless Local Petrov–Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains using a Heaviside step function as test function. In this case, governing equations corresponding to the stiffness matrix do not involve any domain integration or singular integrals. Nodal points are distributed in the 3D analyzed domain and each node is surrounded by a cubic sub-domain to which a local integral equation is applied. The meshless approximation based on the three-dimensional Moving Least-Square (MLS) is employed as shape function to approximate the field variable of scattered nodes in the problem domain. The Newmark time integration method is used to solve the system of coupled second-order ODEs. Effective material properties of the plate, made of two isotropic constituents with volume fractions varying only in the thickness direction, are computed using the Mori–Tanaka homogenization technique. Numerical examples for solving the static and dynamic response of elastic thick functionally graded plates are demonstrated. As a result, the distributions of the deflection and stresses through the plate thickness are presented for different material gradients and boundary conditions. The effects of the volume fractions of the constituents on the centroidal deflection are also investigated. The numerical efficiency of the proposed meshless method is illustrated by the comparison of results obtained from previous literatures.

نویسندگان

A. Rezaei Mojdehi [ Wind Turbines Technology Development Center, Niroo Research Institute, Tehran, Iran ]

A. Darvizeh [ Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Anzali Branch, Bandar-e-Anzali, Iran ]

A. Basti [ Department of Mechanical Engineering, Faculty of Engineering, The University of Guilan, Iran ]

H. Rajabi [ Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Lahijan Branch, Lahijan, Iran ]

کلمات کلیدی

Meshless local Petrov–Galerkin method Thick functionally graded plates Three dimensional moving least square approximation Static and dynamic analysis

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Engineering Analysis with Boundary Elements

This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.

حوزه های تحت پوشش : Boundary Elements