Application of Polynomial Reproducing Scheme to Non-Linear Mechanics

Designing advanced engineering systems requires the use of Computer aided tools. The simulation requires solving partial differential governing equations. Traditionally such equations are largely solved using numerical methods like FDM or FEM, where in the spatial domain has to be discretized into meshes. Afore mentioned methods need a predefined mesh to work with. They can not handle large deformation problems, crack propagation problems etc. Using the theory of Cosserat rod and applying mesh free methods we could solve numerous problems and could accurately capture the large deformations which usual FEM packages can not. A novel method for derivation of mesh free shape functions called ERKM (Error reproducing kernel method) has been implemented. We are currently working on a problem with the objective of capturing twist bifurcation points in a cable. Many the problems that can be solved by FEM can now be handled with more ease.Challenges faced. Finding a novel way of formulating the mesh free shape functions which can reproduce polynomial of the required degree was a challenge