Proper Generalized Decomposition for Parametric Study and Material Distribution Design of Multi-Directional Functionally Graded Plates Based on 3D Elasticity Solution

The use of mesh-based numerical methods for a 3D elasticity solution of thick plates involves high computational costs. This particularly limits parametric studies and material distribution design problems because they need a large number of independent simulations to evaluate the effects of material distribution and optimization. In this context, in the current work, the Proper Generalized Decomposition (PGD) technique is adopted to overcome this difficulty and solve the 3D elasticity problems in a high-dimensional parametric space. PGD is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations, which can be solved easily. Moreover, PGD makes it possible to perform parametric solutions in a unified and efficient manner. In the present work, some examples of a parametric elasticity solution and material distribution design of multi-directional FGM composite thick plates are presented after some validation case studies to show the applicability of PGD in such problems.

Failure Analysis of Multi-Layered Thick-Walled Composite Pipes Subjected to Torsion Loading

In the current study multi-layered thick-walled fibre reinforced composite pipes under torsion loading are considered. To analyse the stress-strain distribution in the pipe the Finite Element model (ABAQUS) has been developed. Using the model the radial, hoop, axial and shear stresses have been calculated for different lay-ups of the fibre reinforced pipes, and modified Tsai-Hill failure coefficients have been computed. The validation of the model was done by comparing the results available in the literature and the semi-analytical three-dimensional elasticity solution. The dependence of the failure coefficient on winding angles and layers’ thickness was investigated and analyzed, and the appropriate design considerations have been suggested for four-layer pipes.

Flexure of a rigidly clamped orthotropic sandwich plate strip – An elasticity solution using superposition method

A simple two-dimensional elasticity solution is presented here for flexure of an infinite sandwich strip with rigidly clamped ends; it is based on the superposition of a strong form solution for a simply supported strip under transverse loading and a Ritz solution for end-loading. Results useful for future comparisons are presented in tabular form. On the basis of these results, the accuracy of classical plate theory and first-order shear deformation theory is critically examined. Finally, the difference between rigidly clamped end conditions and a softer version of clamped conditions is highlighted with reference to far-field response.

A novel finite element formulation based on extended higher-order theory for sandwich plates of arbitrary aspect ratio

The extended higher-order sandwich plate theory for plates with arbitrary aspect ratio was formulated for two-dimensional orthotropic sandwich plates. The novelty of the theory is that it considers five generalized co-ordinates in the core (two axial and one transverse displacements at centroid of the core, one rotation at the centroid of the core about x-axis and one rotation at the centroid of the core about y-axis). Theory is very accurate when compared with the exact elasticity solution in terms of stresses and displacement both. In the current paper, a novel two dimensional rectangular element is developed based on the extended higher-order sandwich plate theory. Elemental equations along with the procedure to derive these is given in the paper. Developed finite element model is validated by comparing the results with elasticity solution and the theory itself for two sandwich plate configurations. The comparison shows that results obtained from the proposed finite element are in very good agreement with elasticity in terms of displacements and stresses both. Thus the proposed element is a powerful analysis tool which can be used for accurately analyzing the real world structures involving sandwich plates at a low computational cost.