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# On Static Analysis of Composite Plane State Structures via GDQFEM and Cell Method

E. Viola1, F. Tornabene1, E. Ferretti1, N. Fantuzzi1
1 DICAM Department, University of Bologna, Italy.

Computer Modeling in Engineering & Sciences 2013, 94(5), 421-458. https://doi.org/10.3970/cmes.2013.094.421

### Abstract

In this paper, an advanced version of the classic GDQ method, called the Generalized Differential Quadrature Finite Element Method (GDQFEM) is formulated to solve plate elastic problems with inclusions. The GDQFEM is compared with Cell Method (CM) and Finite Element Method (FEM). In particular, stress and strain results at fiber/matrix interface of dissimilar materials are provided. The GDQFEM is based on the classic Generalized Differential Quadrature (GDQ) technique that is applied upon each sub-domain, or element, into which the problem domain is divided. When the physical domain is not regular, the mapping technique is used to transform the fundamental system of equations and all the compatibility conditions. A differential problem defined on the regular master element in the computational domain is turned into an algebraic system. With respect to the very well-known Finite Element Method (FEM), the GDQFEM is based on a different approach: the direct derivative calculation is performed by using the GDQ rule. The imposition of the compatibility conditions between two boundaries are also used in the CM for solving contact problems. Since the GDQFEM is a higherorder tool connected with the resolution of the strong formulation of the system of equations, the compatibility conditions must be applied at each disconnection in order to capture the discontinuity between two boundaries, without losing accuracy. A comparison between GDQFEM, CM and FEM is presented and very good agreement is observed.

### Keywords

Generalized Differential Quadrature Finite Element Method, Inclusion problem, Boundary Value Problem, Cell Method.

Viola, E., Tornabene, F., Ferretti, E., Fantuzzi, N. (2013). On Static Analysis of Composite Plane State Structures via GDQFEM and Cell Method. CMES-Computer Modeling in Engineering & Sciences, 94(5), 421–458.

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