A Novel Finite-Element– Numerical-Integration Model for Composite Laminates Supported on Opposite Edges

Abstract

An attempt is made here to devise a new methodology for an integrated stress analysis of laminated composite plates wherein both in-plane and transverse stresses are evaluated simultaneously. The method is based on the governing three-dimensional (3D) partial differential equations (PDEs) of elasticity. A systematic procedure is developed for a case when one of the two in-plane dimensions of the laminate is considered infinitely long (y direction) with no changes in loading and boundary conditions in that direction. The laminate could then be considered in a two-dimensional (2D) state of plane strain in x-z plane. It is here that the governing 2D PDEs are transformed into a coupled system of first-order ordinary differential equations (ODEs) in transverse z direction by introducing partial discretization in the finite inplane direction x. The mathematical model thus reduces to solution of a boundary value problem (BVP) in the transverse z direction in ODEs. This BVP is then transformed into a set of initial value problems (IVPs) so as to use the available efficient and effective numerical integrators for them. Through thickness displacement and stress fields at the finite element discrete nodes are observed to be in excellent agreement with the elasticity solution. A few new results for cross-ply laminates under clamped support conditions are also presented for future reference and also to show the generality of the formulation.

Application of refined mixed finite element model for analysis of laminated composite beams

“…Transverse displacement w and inplane stress σ x shows agreement up to some extent. Transverse shear stress τ xz seems more physically intuitive in the case of present formulation as compared with Kant [13]. Only a finite element scheme is asymmetric double layer laminated beam with lamina scheme of (0 • /90 • ) which is clamped at both ends, material properties given by Pagano [1] and subjected to sinusoidal load and compared with the available solution given by Kant [13] Figure 3.…”

“…In the numerical example, clamped composite unsymmetric and symmetric laminates with lamina scheme of (0 3 shows the through-thickness variation of different parameters and compared with Kant [13] and Ramtekkar and Desai [10]. Transverse displacement w and inplane stress σ x shows agreement up to some extent.…”

“…Only a finite element scheme is asymmetric double layer laminated beam with lamina scheme of (0 • /90 • ) which is clamped at both ends, material properties given by Pagano [1] and subjected to sinusoidal load and compared with the available solution given by Kant [13] Figure 3. Distribution of normalised (a) in-plane stress σ x (b) transverse displacement W (c) transverse shear stress τ xz (d) transverse normal stress σ z in the thickness direction for symmetric tripple layer laminated beam with lamina scheme of (0 • /90 • /0 • ) which is clamped at both ends, material properties given by Pagano [1] and subjected to sinusoidal load and compared with the available solution given by Kant [13] and Ramtekkar and Desai [10]…”

“…Figure 2. Distribution of normalised (a) in-plane stress σ x (b) transverse displacement W (c) transverse shear stress τ xz (d) transverse normalstress σ z in the thickness direction for asymmetric double layer laminated beam with lamina scheme of (0 • /90 • ) which is clamped at both ends, material properties given by Pagano[1] and subjected to sinusoidal load and compared with the available solution given by Kant[13] …”

Cylindrical bending of piezoelectric laminates with a higher order shear and normal deformation theory

“…Results are presented for laminates simply supported on all edges and under cylindrical bending. Kant et al [27][28][29] also presented a new partial discretization mixed FE formulation for general laminates with any boundary conditions. Present results for non-piezoelectric plates under plane strain condition are compared with the elasticity [35], semi-analytical [26,30], partial FE [27][28][29][30] and Reissner and Mindlin [10,11] (FOST) solutions.…”