Arch Appl Mech DOI 10.1007/s00419-016-1222-9 ORIGINAL Pravin Bhad · Vinod Varghese · Lalsingh Khalsa A modified approach for the thermoelastic large deflection in the elliptical plate Received: 18 August 2016 / Accepted: 8 December 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract The present paper deals with an investigation into the thermoelastic effect on the elliptical plate during large deflection while heating with non-stationary temperature distribution. The governing equation for the deflection is formulated with modification within the existing methodology devised by Berger. Thermally induced deflection results and its associated stresses are obtained in terms of Mathieu function of the first kind of order 2n. Furthermore, aforementioned problems can be degenerated into the problems of the circular region by applying limiting conditions. Some results which are derived by means of computational tools are illustrated numerically and depicted graphically. Keywords Elliptic plate · Temperature distribution · Large deflection · Thermal stresses · Mathieu function · Berger’s method 1 Introduction As far as theoretical mechanics is concerned, the solution methods for nonlinear differential equations play a very crucial role as many problems have been modelled using such equations. In particular, large deflection for any structural profile subjected to pressure load or thermal impact can be described by the same nonlinear differential equation. The problem of large deflections has attracted a lot of attention, and few different methods have been suggested to solve it. A short history of the research work associated with the large deflection insights various approximate methods such as the Ritz energy method, Galerkin’s Method, finite element models and perturbation theory to solve the system. Two highly cited literature reviews on large deflection were considered by Chia [1] and Sathyamoorthy [2] in their books. The uniformly loaded homogeneous and isotropic plate has attracted the focus of the researchers over the past long time because of its application to numerous machines and structures. The published studies mostly have been modelled by the classical theory of thin plates supported at isolated points along the edges [3, 4] because of the classical plate bending theory [5]. Of most recent literature, some authors have undertaken the work on nonlinear bending analysis, which can be summarised as given below. Altekin [6] analysed the nonlinear bending analysis of clamped circular plates by the Newton–Raphson method. Nishawala [7] in his thesis discussed nonlinear bending of simply P. Bhad (B ) Priyadarshini J. L. College of Engg., Nagpur, India E-mail: praash.bhad@gmail.com V. Varghese RTM Nagpur University, Nagpur, India L. Khalsa M.G. College, Armori, Gadchiroli, India