Chapter 6 - Large deflection analysis of poroelastic beams

Abstract

The chapter discusses large deflections of beams. The deflection is considered to be small, and thus linear theories are sufficient when the constitutive law is linear, for some situations, it may be necessary to employ a large deflection theory in order to correctly describe the behavior of the structure. On the other hand, the deformation can still be small and yet the skeletal material behaves elastically; the large deflection is made possible by the slenderness of the components. Therefore, the components are modeled geometrically non-linear but constitutively linear. Biot's constitutive law and Darcy's law are adopted in the linear theory, while new geometrical relations and equilibrium equations are necessarily introduced. In the large deflection case, the stretching and bending problems are coupled. The non-linear boundary value problem is solved numerically by using the finite difference method with respect to the spatial coordinate and using a simple successive implicit formula (the trapezoid formula) to deal with the time variable. Several types of geometrical and diffusion boundary conditions are investigated by means of numerical solutions.