A Unified Approach to the Finite Element Method and Error Analysis Procedures

Introduction to The Strain Gradient Reformulation of the Finite Difference Method

Introduction

The theoretical basis and practical application of the error measures developed in Part V depend on the ability to form finite difference operators for the nodal patterns found in finite element meshes. The ability to form these derivative approximations emerges as a corollary to the strain gradient approach to the finite element method. We see in Part IV that the finite difference operators are contained in the transformations from nodal displacements to strain gradient quantities. The finite difference operators are produced when the [Φ] matrix is inverted. The ability to compute the finite difference operators in a routine manner ensures that the ...