2024 Volume 80 Issue 2 Article ID: 23-00040
This paper states for framed structures, that we can compute both stresses and displacement of structures directly, using a saddle point matrix. And in this paper, it is stated that contributions of each element for responses can be computed simultaneously. Those contributions of each element represent actions of each element explicitly. And, contribution analysis for frequencies of structures, formulated from eigenvalue analysis, are stated. In addition, when sensitivity coefficients of responses are necessary, for example, in optimal design and structural analysis, they are computed immediately by dividing contribution factor by contribution variable (in this paper, element stiffness). In the past, formulation of contribution analysis and sensitivity analysis are performed from stiffness equation, but in this paper, they are formulated without deleting the stress from three fundamental equations of equilibrium of structures. And, in this paper, all the contributions are considered for external work.
