Discrete spatial simulations in structural mechanics and in environmental problems

Abstract

Digital simulations of random variables or random fields in conjunction with probabilistic methods can be regarded as powerful tools in the analysis of the reliability of nonlinear models of structures and in modelling of environmental problems. In this paper three civil engineering problems are presented and solved using the same methodology of random sampling. The first problem concerns the stability of nonlinear randomly imperfect structures with special attention paid to the probability distribution of the limit loads. The second problem is devoted to the analysis of the effect of the material and load imperfections on the response of nonlinear shell structures. The third problem deals with the theoretical reconstruction of physical processes in soil, water or air on the basis of limited, fragmentary observed data. This paper presents a unified approach to solutions of nonlinear equations arising in time-independent discrete models with random parameters.