Load paths visualization in plane elasticity using load function method

The paper proposes a load function method for load path visualization and load flow calculation in plane elasticity problems. The load functions are directly derived from 2D equilibrium equations. The stresses are written in terms of the load functions and the load flow is calculated using the load function gradient. The load functions are defined using generalized Beltrami representation. A constructive proof is given for the existence of load functions. A set of Poisson's equations in terms of load functions and stress components are developed and an efficient numerical procedure to solve them is discussed. Numerical results show the proposed load function method is able to define the load paths and obtain the load flow using an Airy stress function for problems with available closed form solution, and also can be easily integrated into the numerical approaches to calculate load paths for complex problems.