Stochastic First-ply Failure Analysis of Laminated Composite Plates Under in Plane Tensile Loading Appaso M Gadade 1, a , Achchhe Lal 2, b and B N Singh 3, c 1, 2 Department of Mechanical Engineering, S.V. National Inst. of Technology, Surat-395007, India 3 Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur-721302, India a appagadade@yahoo.com, b achchhelal@med.svnit.ac.in, c bnsingh@aero.iitkgp.ernet.in Keywords: Laminated composite plate, First-ply failure loads, Random system properties, stochastic finite element method. Abstract. The present work deals with second order statistics of first-ply failure response of geometrically nonlinear laminated composite plate subjected to in-plane tensile loading with random system properties. System properties such as the material properties and lamina plate thickness are modeled as independent random variables.The mathematical formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear kinematics. An efficient C 0 nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is extended successfully and applied for failure problem in random environment and is employed to evaluate the dimensionless mean failure load and variance of failure index by modeling the system properties as basic random variables using Tsai- Wu and Hoffman failure criteria.Typical numerical results are presented to examine the effect of amplitude ratios, boundary conditions, lamination schemes with random system properties for different failure criterion.The results obtained using present solution approach is validated with the results available in the literatures. Introduction Composite laminates being orthotropic material involves large number of parameters. Complete control over all these parameters is not economically feasible and variations in the material and geometric parameters in these laminate are inherent. This uncertainty in the system parameters gives rise to uncertainty in the response behavior. For certain sensitive applications such as aerospace, accuracy in response behavior of composite laminate is achieved by modeling such type of problems with random material properties and nonlinear deflection behavior. Therefore there is a need of efficient and accurate analysis technique which takes care of inherent material scatter and random material properties. This is possible by extending stochastic finite element method with uncertain material properties to failure problems. The present work is an attempt to incorporate the nonlinear effects in random environment for failure problem. The second order statistics of failure response for composite plate with random material properties under in plane deterministic tensile loading has been evaluated. The analysis uses HSDT and Von-Karman non-linear strain displacement relationship with FOPT. Perturbation technique The governing can be written in the most general form as [1] { } { } R R K W F   =     (1) where R K       , { } R W and { } F are represented as the random stiffness matrix, the random displacement response vector and deterministic forcing vector respectively and superscript ‘R’ denotes random. Any random variable can be expressed as the sum of its mean and the zero mean random variable Random variable ( ) R RV = mean ( ) d RV + zero-mean random variable ( ) r RV . (2) Advanced Materials Research Vol. 747 (2013) pp 269-272 © (2013) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.747.269 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 123.63.20.130-05/06/13,14:34:33)