Physical Nonlinearity and Anisotropic Features of Materials in Structure Analysis

Abstract

A justified assessment of the work of constructions and their elements should take into account physical and mechanical characteristics of construction materials. Although taking physical nonlinearity and anisotropic features into consideration will make the design more complicated, it is strongly needed to develop tools and methods that cover all the specific features of the material more precisely. Mathematical methods of construction design that take physical nonlinearity into account are quite well investigated. They are: Newton Raphson method; modified Newton Raphson method which differs from the original version by the fact that the stiffness matrix has to be calculated only once at the first iteration and remains the same for several further iterations and steps of load; the method of growing stiffness which is quite efficient in dealing with problems of physical nonlinearity, and so on. But certain difficulties appear as we consider these problems from the point of view of physics: the majority of strength and plastic-yield criteria are not implemented in design process yet. That is caused by complicated mathematics and a need for more experiment in order to determine the constants in use.