DIRECT COMPUTATION OF THE DESIGN POINT OF A STOCHASTIC STRUCTURE USING A FINITE-ELEMENT CODE

In a probabilistic analysis of a stochastic structure, it is important to identify the design point-the point of most probable failure. When both the resistance and load term of the limit state function are random, a modified joint probability density function is formulated, and the design point is obtained by searching for the maximum point of this function. The modification is done by introducing the finite element solution for the load term into the original basic joint probability density function of the random variables. For threshold value problems, the design point is obtained by searching for the maximum point of the original joint probability function, conditional upon the finite element solution being equal to the threshold value. Once the design point is identified, the index of reliability can be found using known techniques for structures with independent and dependent random variables, normally and non-normally distributed. The solution is obtained without the need for any derivatives of the load term with respect to the random variables, thus no modifications are required in the finite element code used. The solution requires an algorithm that finds the maximum value of the objective function in a well defined variable space. Several numerical examples are presented, including cases of random fields, which are discretized by stochastic finite element into random variables. The library module of design optimization of the finite element code employed (ANSYS) is used to find the design point. Applying the proposed method permits the designer to perform probabilistic analysis with computational tools already available.