This paper presents a static analysis of functionally graded (FG) single and sandwich beams by using a simple and ef cient 4-unknown quasi-3D hybrid type theory, which includes both shear deformation and thickness stretching effects. The governing equations and boundary conditions are derived by employing the principle of virtual works. Navier-type closed-form solution is obtained for several beams. New hybrid type shear strain shape functions for the inplane and transverse displacement were introduced in general manner to model the displacement eld of beams. Numerical results of the present compact quasi-3D theory are compared with other quasi-3D higher order shear deformation theories (HSDTs).

This paper presents a static analysis of functionally graded single and sandwich beams by using an ef cient 7DOFs quasi-3D hybrid type theory. The governing equations are derived by employing the principle of virtual works in a weak form and solved by means of the Finite Element Method (FEM). A C1 cubic Hermite interpolation is used for the vertical de ection variables while C0 linear interpolation is employed for the other kinematics variables. Convergence rates are studied in order to validate the nite element technique. Numerical results of the present formulation are compared with analytical and FEM solutions available in the literature.

This paper presents Best Theory Diagrams (BTDs) employing combinations of Maclaurin, trigonometric and exponential terms to build two-dimensional theories for laminated cross-ply plates. The BTD is a curve in which the least number of unknown variables to meet a given accuracy requirement is read. The used refined models are Equivalent Single Layer and are obtained using the Unified Formulation developed by Carrera. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier-type closed form solutions have been obtained in the case of simply supported plates loaded by a bisinuisoidal transverse pressure. BTDs have been constructed using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The influence of trigonometric and exponential terms in the BTDs has been studied for different layer configurations, length-to-thickness ratios and stresses. It is shown that the addition of trigonometric and exponential expansion terms to Maclaurin ones may improve the accuracy and computational cost of refined plate theories. The combined use of CUF, AAM and GA is a powerful tool to evaluate the accuracy of any structural theory.

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This paper presents Best Theory Diagrams (BTDs) for plates considering all the displacement and stress components as objectives. The BTD is a diagram in which the minimum number of terms that have to be used to achieve the desired accuracy can be read. Maclaurin, zigzag , trigonometric and exponential expansions are employed for the static analysis of cross-ply composite plates. The Equivalent Single Layer (ESL) approach is considered, and the Unified Formulation developed by Carrera is used. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier-type closed form solutions are adopted. BTDs are obtained using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The results show that the BTD can be used as a tool to assess the accuracy and computational efficiency of any structural models and to draw guidelines to develop structural models. The inclusion of the multiobjective capability extends the BTD validity to the recognition of the role played by each output parameter in the refinement of a structural model.