Abstract
A method to put the exact deformation of elastic structures between the upper and lower bounds is proposed. This method is based on the following three conceptions : (i) The rigid and soft side models of elastic structures, defined in this paper. (ii) The property of the matrix of positive semidefinite quadratic forms. (iii) The principles of total potential and complementary energy. Then, every element of the compliance matrix of an original elastic structure is put between the upper and lower bounds, which can be calculated with the solution of the idealized rigid or soft side model. The upper and lower bounds of the deformation of the elastic structure, which can not be solved exactly, can be derived by using the above mentioned matrix for actual load conditions. This method can be used also to make simply the approximate solution with the error estimation for a complicated solvable or unsolvable structure.
