Lithospheric Flexure

This chapter shows how the finite element method (FEM) can be applied to solve problems involving flexural deformation of the lithosphere in three‐dimensions (3Ds). The various forms of the flexure equation are important because they enable one to predict in a simple manner how the lithosphere responds to different load scenarios. In addition, the equations can be used to constrain the elastic properties of the lithosphere in cases when the loads and deflections are known. The single program listed in the chapter can be used to study full 3D flexure with in‐plane forces, spatially variable loads, and variable flexural rigidity, as well as more restricted situations. Following the formulation presented by Zienkiewicz and Taylor, the chapter introduces the standard finite element approximation. It explains the practical problem of how to solve the discretized flexural problem with Matlab. A single stand‐alone Matlab script is discussed in detail, which enables various practical problems to be investigated.