A semi-analytical interval method for response bounds analysis of structures with spatially uncertain loads

This paper proposes a semi-analytical interval method for static response bounds analysis of structures subjected to spatially uncertain loads. In the investigated problem, the external loads applied to the structure are spatially uncertain but bounded, which are quantified by an interval field model using upper and lower bounds. By introducing the interval field and its series expansion form into finite element analysis, the interval finite element equilibrium equations are then formulated, where the force vector is an interval vector. Solving the interval equations by the proposed method, a semi-analytical solution of the upper and lower bounds of structural static responses such as displacement and stress can be obtained efficiently. Finally, the effectiveness and accuracy of the proposed method are verified by three numerical examples.