A quadratic temporal finite element method for linear elastic structural dynamics

Recently, in order to overcome the key shortcoming in Hamilton’s principle, the extended framework of Hamilton’s principle was formulated. This new variational framework provides a sound base to develop novel temporal finite element methods with the proper use of initial conditions to the strong form. As its initial and practical application in structural dynamic analysis, this paper presents a quadratic temporal finite element method for linear elastic multi-degrees-of-freedom systems. Numerical features of the developed method are analytically and numerically investigated with comparison to the currently dominant method; the results highlight the improved performance of the proposed method.