Bending of laminated plates with mixed boundary conditions based on higher-order shear deformation theory

Abstract

The bending of laminated plates is considered using higher-order transverse shear deformation theory. The principle of virtual work is used to derive a new set of seven governing equations and corresponding boundary conditions. These equations, combined with eighteen relationships between the resultant stress and displacement components, compose a system of first-order partial differential equations that is solved by the generalized differential quadrature method. Numerical results for laminated plates with a variety of mixed boundary conditions are calculated using the proposed method, and good agreement is found with the corresponding solutions obtained using ANSYS.

Developing an element free method for higher order shear deformation analysis of plates

“…Using the procedure provided in [30], the relationship between strain components and seven field variables for HSDT plate in the matrix form can be written as In Eq. (2), two new unknown functions w i ¼ ∂w=∂x i ði ¼ 1; 2Þ have been introduced to simplify stiffness matrix calculations.…”

“…Then, decomposing the stiffness matrix in order to use different integration points for numerical integration along with a linear basis for MLS approximation can produce accurate results even for thin plates. Table 3 shows the comparison of the results using proposed approach (EFG) versus FEM [34] and the Generalized Differential Quadrature (GDQ) proposed in [30]. Both FEM and GDQ utilize HSDT.…”