Published Paper


Avariational Formulation and Navier's Method for Solving Laminated Plate Problems

Sanjay Kantrao Kulkarni
Symbiosis Institute of Technology (SIT), Symbiosis International (Deemed University), Lavale, Pune-412115
Page: 325-333
Published on: 2025 September

Abstract

In case of laminated platesdetermination of stresses and displacements under thermal loads is important as it results in delamination under thermal loads. One has to develop the equations of motion or governing equations before computing thermal deformations. A variational formulation or virtual work method is useful tool to develop the governing equations. Once the governing equations are established, Navier’s method is required to apply for the determination of displacements and stresses under thermal load. A Navier’s method assumes trigonometric solution that satisfy the boundary conditions. This combination (variational formulation and Navier’s method) is a powerful analytical tool for solving laminated plate problems. A variational formulation is widely used in structural mechanics especially for composite laminates. Some of the structural theories like classical, first order, higher order and layer-wise theories are using virtual work method or variational formulation for laminated plates. This method consists of mainly three vital point as given below. An application of virtual work principle or virtual formulation to composite laminated plates. Use of integration by parts for further solution and development of governing equations. Apply Navier’s method to obtain thermal deformations (stresses and displacements) in the laminated composite plate.

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