Advanced Numerical Modeling for Plate/Shell Structures with Multicomponent and Composite Materials--Meshless Technique Approach

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Functionally graded materials (FGMs) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. This results in continuously graded thermal and mechanical properties at the (macroscopic) structural scale. FGMs posses some advantages over conventional composites because of their continuously graded structures and properties. Due to the high mathematical complexity of the initial-boundary value problems, analytical approaches for the FGMs are restricted to simple geometry and boundary conditions. Thus, analyses in FGM demand accurate and efficient numerical methods. The finite element method can be successfully applied to problems with an arbitrary variation of material properties by using special graded elements. In commercial computer codes, however, material properties are considered to be uniform on each element. The boundary element method (BEM) is a suitable numerical tool for this purpose, too. However, for a general continuously nonhomogeneous body the fundamental solution for many governing equations are not available. Recently, meshless methods are becoming popular, and they have been successfully applied to 2-D and 3-D axisymmetric transient heat conduction analyses for isotropic and anisotropic FGMs and in elasticity. During the last several decades, laminated composite plates have been widely used in engineering structures. All previous BEM applications are dealing with isotropic Reissner-Mindlin plates. In spite of the great success of the FEM and the BEM as accurate and effective numerical tools for the solution of boundary or initial-boundary value problems in domains with complex shapes, there is still a growing interest in developing new advanced numerical methods. Meshless approaches for problems of continuum mechanics have attracted much attention during the past decade especially owing to their high adaptivity and low costs to prepare input data for numerical analyses. Many meshless methods are derived from a weak-form formulation on global domain or a set of local subdomains. In the global formulation background cells are required for the integration of the weak-form. In methods based on local weak-form formulation no cells are required and therefore they are often referred to as truly meshless methods. Meshless approximation of the generalized displacements on a simple domain, based on the Moving Least-Squares (MLS) method, allows for elegant and efficient numerical integration of the domain-integral. Several quasi-static boundary value problems have to be solved for various values of the Laplace-transform parameter. The Stehfest's inversion method is applied to obtain the time-dependent solution. The novelty of the proposed project can be stated as:(1) The proposed meshless LIE will be developed for the first time in FGM plates and shells with anisotropic properties.(2) Non-stationary conditions are considered.(3) The method has no limitations on the geometry, material gradation, isotropic or anisotropic properties and loading conditions. (4) Coupling of thermo-mechanical fields can be considered too.