Plenary Lecture

The use of Integral Transforms for analytic solution of pre-stressed thin plate on elastic foundation under axisymmetric loading

Professor Dimitrios G. Pavlou
Technological Institute of Halkida (TEI-Halkida)
Faculty of Mechanical Engineering
34 400 Psahna, Halkida, Evoia
Greece
E-mail: dpavlou@teihal.gr

Abstract: In the past, the model of a thin plate on an elastic foundation was mainly used in structural applications. Currently, thin plates or films of metal, ceramic or synthetic materials are bonded in the surface of machine structural parts or electronic devices to improve their mechanical, thermal, electronic or tribological properties. At these applications, the sub-grade of the thin plate can be simulated as a Winkler-type foundation, which reacts with pressure proportional to the deflection of the plate at each point. The plates in the above applications are loaded by vertical (distributed or concentrated) loads or bending moments, as well as by in-plane forces (compressed or stretched) due to e.g. temperature effects. A large number of analytical or numerical research works have been published to solve several boundary value problems of a classical thin plate or a thin plate on an elastic foundation. However, few research works have been published concerning the differential equation of a pre-stressed thin plate on an elastic foundation, due to its complexity. In the present work, an exact solution of the problem of an infinite circular thin plate on an elastic foundation under combined axisymmetric vertical and radial in-plane forces is attempted. For this purpose, the Hankel’s integral transforms and generalized functions properties are used. Numerical examples are included.
 

Brief Biography of the Speaker:
Dimitrios G. Pavlou is Professor of Metallic Structures and Applied Mechanics in the Faculty of Mechanical Engineering of the Technological Institute of Halkida –TEI Halkidas– Greece (website: www.teihal.gr). Undergraduate degree in Mechanical Engineering and PhD in Fracture Mechanics at the University of Patras. He has extensive industrial experience in engineering design and many years of experience in teaching Strength of Materials (theory and experimental exercises), Fracture Mechanics, Metallic Structures, Structural Analysis and Material Science at the Hellenic Air-Force Academy, University of Piraeus, University of Patras and Technological Institute of Halkida. He has been the General Manager of the VIOTE S.A. (Viotia’s Prefecture Company for Industrial Development), Head of the Secretary of the Research Centre of the University of Piraeus and Chair of the Faculty of Mechanical Engineering of the Technological Institute of Halkida. Pavlou has been on the Faculty of the TEI of Halkida since 1999 and is currently Visiting Professor in the “Polytechnic” University of Timisoara, Romania. He is (a) author of numerous research articles in referee journals and international conferences, (b) author of national and international books covering fracture mechanics, metallic structures, damage mechanics and strength of materials, and (c) referee of numerous research works submitted in international journals and conferences. His research interests are (a) Analytical and Numerical methods in Fracture Mechanics with special emphasis in solution of Boundary Integral Equations (BIE) using Green’s functions and BEM, (b) Damage Mechanics with special emphasis in Fatigue and Creep Damage Accumulation under variable loading as well as life-time prediction of structural parts in service conditions, and (c) Analysis of elastostatic problems using Integral Transforms with special emphasis οn Hankel Transforms.