Proof of Tienstra's Formula by Finite-Element Method

Abstract

Tienstra's formula is proven with a familiar idea, namely, natural coordinates in the finite-element method are the starting points. The proof is completed by an interesting application of modern computing technology—symbolic computation. This proof is a beautiful fusion of elements from surveying, structural analysis, and symbolic computation. Compared to the old proof found in the literature, this new one should be more readable and interesting to students, engineers, and researchers in civil engineering, especially those who have been exposed to the finite-element method.