A new triangular element to model inter‐laminar shear stress continuous plate theory

Abstract

SUMMARYAn efficient triangular element based on an inter-laminar shear stress continuous plate theory is developed and applied to the analysis of composite and sandwich plates under different situations to study the performance of the element. The plate theory represents parabolic through thickness variation of transverse shear stresses where the continuity condition of these stresses are satisfied at the layer interfaces. It also satisfies transverse shear stress free condition at the top and bottom surfaces of the plate. The most attractive feature of the plate theory is that the basic unknowns are same as those used in first-order shear deformation theory. The only problem lies with this elegant plate theory is found in its finite element implementation, as it requires C 1 continuity of transverse displacement at the element interfaces. This is a well-known problem of thin plate elements, which is also found in some other refined plate theories. Although there are some elements based on these refined plate theories but the number of such elements is very few and they possess certain drawbacks in general. Keeping these aspects in view, an attempt has been made in this study to develop a six-noded triangular element having equal degrees of freedom at each node.

A New C0 2D Fe Model Based on Improved Higher Order Zigzag Theory for the Analysis of Soft Core Sandwich Plate

“…The value of w at the plate center, xx  at x= (a + bsin α)/2, y=(bcos α)/2, z=h/2 (Fig.12), and yz  at x=a/2, y=0, z=0.4h obtained in the present analysis are presented in Tab.7. For the skew angle (α) of 0˚, the present results are compared with the 3D elasticity solution (Pagano, 1970) which shows a good correlation between them and for skew angles (α) of 15˚, 30˚, 45˚ and 60˚, the results are in good agreement with the results reported by Chakrabarti and Sheikh (2004). …”

“…A triangular element was presented by Chakrabarti and Sheikh (2004) based on the zigzag theory, which shows excellent performance though the element does not satisfy the normal slope continuity requirement. Akhras and Li (2007) developed a spline finite strip method based on Cho's higher order zigzag theory for the static analysis of the plate.…”

Buckling analysis of laminated composite plates using an efficient C0 FE model

“…In the first-order shear deformation theory (FSDT) a shear correction factor is used to compensate for the assumed uniform transverse shear strain variations over the entire plate thickness. For a better representation of the transverse shear deformations, various higher-order shear deformation (HSDT) plate theories [5,15,16,30,36] were proposed. However, it has been observed and mentioned by many researchers [3] that increasing the number of terms in the in-plane displacement components does not improve the results and it is required to add the effect of inter-laminar transverse shear stress continuity in a multilayered composite plate problem.…”

A new zig-zag theory and C0 plate bending element for composite and sandwich plates

“…In addition to the aforementioned zig-zag theories, Kapuria [15] and Kapuria et al [16,17] also developed the zig-zag theories to analyze the static and the dynamic behaviors of laminated composite plates. More discussion on the zig-zag theories can be found in the article [18][19][20].…”