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

Introduction to Physically Interpretable Notation

Introduction

The interpolation polynomials that model the displacements in the continuum are central to the finite element method. These displacement approximations are differentiated according to the strain-displacement relations to produce the strain representations. The resulting strain models are then used in the formulation of the individual stiffness matrices.

In the standard approach for forming finite element stiffness matrices, the arbitrary coefficients of the displacement polynomials have no specific meaning.¹ Consequently, these arbitrary quantities provide no direct assistance in evaluating the accuracy of the equations being derived. The coefficients are passively carried along ...