Design sensitivity analysis of multi-span non-linear elastic beam–columns with elastic supports

Abstract

The incremental problem arising from the design perturbation of a materially non-linear elastic beam–column with intermediate supports and elastic end supports is formulated via a second variation of the potential energy functional, augmented with constraint conditions. Design variables are distributed parameters (bending stiffness and transverse load), discrete (compression force, end points dead loads and elasticity of supports) and domain (length and intermediate support points). The state variables perturbations are the solution of an incremental BVP (equilibrium differential equation, static, kinematic and jump conditions) derived from an incremental virtual work equation. A sensitivity formula is obtained by the adjoint method.