Through‐the‐thickness stress predictions for laminated plates of advanced composite materials

Abstract

A finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures. Plate element behaviour is specified by prescribing independently the neutral surface displacements and rotations, thus relaxing the Kirchhoff hypothesis. Numerical efficiency is achieved due to the simplicity of the element formulation, i.e. the approach yields a displacement dependent multi-layer model. In-plane layer stresses are determined via the constitutive equations, while the transverse shear and short-transverse normal stresses are determined via the equilibrium equations. Accurate transverse stress variations are obtained by appropriately selecting the displacement field for the element. A selective reduced integration technique is utilized in computing element stiffness matrices. Static and spectral (eigenvalue) tests are performed to demonstrate the element modelling capability.

Hybrid-interface finite element for laminated composite and sandwich beams

“…5(a-d). It can be seen that the results from the present theory are in very good agreement with the Liou and Sun [42] Engblomand Ochoa [41] Carrera LM4 [21] Carrera EMZC3 [21] x (a / 2, Z) elasticity solution [14]. It should also be noted that the hybrid stress models of Liou and Sun [42] and Carrera and Damasi [20,21] have yielded good results (see Figs.…”

“…The elasticity solution for composite laminates under cylindrical bending by Pagano [14], FE solution using multilayer plate bending element by Engblom and Ochoa [41] and Liou and Sun [42], higher order FE solutions by Lo et al [13] and closed-form solution for bending of laminated plates by Ren [43] have been considered for comparison of results obtained from the present FE model. FE solution using HZZT (EMZC3) and higher order multilayer plate bending (LM4) based on Reissner's mixed variational theorem by Carrera and Demasi [20,21] have also been used for comparison.…”

“…However,the displacement-based models (viz. [13,41]) could not It has been observed that minimum four element rows for each lamina in thickness direction are required for converging solution. The normalized in-plane stress¯ x (a/2, h/2), the maximum transverse stress,¯ xz (max) and the transverse displacement,w(a/2, 0) have been compared in Table 7 The example shows the capability of present formulation to handle sandwich beams effectively.…”

Multi-model finite element scheme for static and free vibration analyses of composite laminated beams

“…Normalized maximum transverse displacement ( w ), in-plane normal stress ( x σ ) and transverse shear stress ( xz τ ) for the simply supported laminated beam (with S = 4 and 10) have been presented in Table 3. Results obtained through present analysis are compared with elasticity solution by Pagano (1969) and various analytical/ FE solutions given by Desai and Ramtekkar (2002); Lo et al (1978); Spilker (1982); Engblom and Ochoa (1985); Toledano and Murakami (1987); Manjunatha and Kant (1993b). Present results shows good agreement with the elasticity solutions, which underlines the usefulness of the present model.…”

“…It is observed that the results from the present multi-model scheme are in very good agreement with the elasticity solution (Pagano, 1969). It is also noted that the displacement based models (Lo et al, 1978;Engblom and Ochoa, 1985), have not been able to predict the in-plane and the transverse stresses. The continuity of the transverse stresses is ensured and the integration of equilibrium equations is advantageously avoided.…”