• Structural Engineering and Mechanics
• /
• v.40 no.2
• /
• pp.191-213
• /
• 2011

This paper presents an improved 8-node shell element for the analysis of plates and shells. The finite element, based on a refined first-order shear deformation theory, is further improved by the combined use of assumed natural strain method. We analyze the influence of the shell element with the different patterns of sampling points for interpolating different components of strains. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Further, a refined first-order shear deformation theory, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. Numerical examples demonstrate that the present element perform better in comparison with other shell elements.

• Computers and Concrete
• /
• v.27 no.3
• /
• pp.269-282
• /
• 2021

A dynamic analytical solution for a simply supported, rectangular functionally graded plate with a porous middle layer under time-dependent load based on a refined third-order shear deformation theory with a cubic variation of in-plane displacements according to the thickness and linear/quadratic transverse displacement is presented. The solution achieved in the trigonometric series form and rests on the Green's function method. Two porosity types and their influence on material properties, and mechanical behavior are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using the power-law distribution idealization. Numerical calculations have been carried out to demonstrate the accuracy of the kinematic model for the dynamic problem, the effect of porosity, thickness of porous layers, power-law index, and type of loading on the dynamic response of an imperfect functionally graded material plate.

• Steel and Composite Structures
• /
• v.18 no.2
• /
• pp.409-423
• /
• 2015

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (${\varepsilon}_Z{\neq}0$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.8 no.4
• /
• pp.107-114
• /
• 2004

In this paper, a simple improved 8-node finite element for the finite element analysis of fibrous composite plates is presented by using the direct modification. We drive explicit expressions of shape functions for the 8-node element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian coordinates. The refined first-order shear deformation theory is proposed, which results in parabolic through-thickness distribution of the transverse shear strains and stresses from the formulation based on the third-order shear deformation theory. It eliminates the need for shear correction factors in the first-order theory. This finite element is further improved by combined use of assumed strain, modified shape function, and refined first-order theory. To show the effectiveness of our simple modification on the 8-node finite elements, numerical studies are carried out the static, buckling and free vibration analysis of fibrous composite plates.

• Steel and Composite Structures
• /
• v.26 no.1
• /
• pp.89-102
• /
• 2018

This work investigates a novel plate formulation and a modified couple stress theory that introduces a variable length scale parameter is presented to discuss the static and dynamic of functionally graded (FG) micro-plates. A new type of third-order shear deformation theory of Reddy that use only 4 unknowns by including undetermined integral variables is proposed in this study. The equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for a simply supported micro-plate. Numerical examples are presented to examine the effect of the length scale parameter on the responses of micro-plates. The obtained results are compared with the previously published results to demonstrate the correctness of the present formulation.