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A two-phase scheme for accurate predictions of interlaminar stresses in laminated plate and shell structures has been addressed in this study. A modified superconvergent patch recovery (MSPR) technique has been utilized to obtain accurate nodal in-plane stresses which are subsequently used with the thickness integration of the three-dimensional equilibrium equations to evaluate the transverse shear and normal stresses. Remarkably, the continuity of the resulting interlaminar stresses is automatically satisfied. Such a two-phase scheme has been applied successfully to a simple smeared layer model (SLM), i.e., a low-order quadrilateral hybrid/mixed element (HMSH5). This simple procedure is found to be completely equivalent to the far more computationally expensive alternative approaches, e.g., sophisticated layerwise approach, for flat geometry. A fairly large number of numerical examples have been solved and the results have shown that the proposed scheme is fairly reliable and computationally cost effective.

In this paper, a simple and accurate sinusoidal trigonometric theory (STT) for the bending analysis of functionally graded single-layer and sandwich plates and shells is presented for the first time. The principal feature of this theory is that models the thickness stretching effect with only 4-unknowns, even less than the first order shear deformation theory (FSDT) which as it is well-known has 5-unknowns. The governing equations and boundary conditions are derived by employing the principle of virtual work. Then, a Navier-type closed-form solution is obtained for functionally graded plates and shells subjected to bi-sinusoidal load for simply supported boundary conditions. Consequently, numerical results of the present STT are compared with other refined theories, FSDT, and 3D solutions. Finally, it can be concluded that: (a) An accurate but simple 4-unknown STT with thickness stretching effect is developed for the first time. (b) Optimization procedure (described in the paper) appear to be of paramount importance for 4-unknown higher order shear deformation theories (HSDTs) of this gender, so deserves a lot of further research. (c) Transverse shear stresses results are sensitive to the theory and need carefully attention.

In this paper, discrete shear gap method (DSG)-based central point of the three-node triangular element (CP-DSG3) is presented for both linear and geometrically nonlinear analysis of plates and shells. A fictitious central point is introduced as the base point of the DSG to overcome the anisotropy of the formerly proposed formulation. In the CP-DSG3, the discrete shear gap at each field node is deduced using rotations of all three nodes in local coordinate system, which makes it an isotropic triangular plate and shell element. At the same time, the CP-DSG3 inherits the advantages of shear-locking-free from the DSG. Moreover, a series of numerical examples consisting of standard patch test, linear and geometrically nonlinear problems have been investigated and the results demonstrate the excellent performance and accuracy of the proposed CP-DSG3.

Within the framework of the shear deformable linear theory of plates and shells we discuss the viscoelastic models of two-dimensional (2D) constitutive equations for the stress resultants (forces and moments). The main goal of the paper focuses on the analysis of the influence of the viscoelastic bulk material behaviour, the through-the-thickness structure of the plate and surface effects on the resultant governing equations. The two-dimensional constitutive equations are represented using the relaxation functions. As an example 2D constitutive equations for plates and shells made of viscoelastic foams are considered. In addition, the functionally graded structures are presented. Finally, we consider the scaling effect in the case of nano-sized foams using the theory of surface stresses.