A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

Numerical approaches for the analysis of timber frame walls

A numerical approach to simulate the behaviour of timber shear walls under both static and dynamic loading is proposed. Because the behaviour of timber shear walls hinges on the behaviour of the nail connections, the force-displacement behaviour of sheathing-to-framing nail connections are first determined and then used to define the hysteretic properties of finite elements representing these connections. The model nails are subsequently implemented into model walls. The model walls are verified using experimental results for both monotonic and cyclic loading. It is demonstrated that the complex hysteretic behaviour of timber shear walls can be reasonably represented using model shear walls in which nonlinear material failure is concentrated only at the sheathing-to-framing nail connections.