Probabilistic Design of Fiber Reinforced Composite with First Order Second Moment Method

Abstract

The presented study is concerned with the probabilistic design method for the strength of the fiber reinforced composite materials under the plane stress state. This method is established by applying the advanced first order second moment (AFOSM) method to the tensor polynomial theory proposed by Tsai and Wu. The laminate composite is treated as a homogeneous and orthotropic material. The tensor polynomial theory is adopted as the failure criterion becauce of covering various theories based on the maximum work criterion. The proposed theory requires only the mean values and the coefficients of variation of both the principal strength components and the applied load by using of AFOSM method. Safety index is used as the scale of reliability in stead of the probability of survival. It is shown that the Lagrange multiplier formulation can be used to evaluate the safety index and the location of the design point. The numercal results by AFOSM method are compared with those by the first order second moment method. Thus, it is obvious that the probabilistic design with AFOSM method is excellent and effective enough for practical use.