General templates for n-noded bar elements based on reduced representations and numerical dispersion reduction by optimized finite elements

Various kinds of finite elements are proposed and employed for one-dimensional wave-field simulations, each of which has their own capabilities and disadvantages. This paper deals with structural similarities and differences that arise at the element level, by the use of reduced forms of mass and stiffness matrices. General parameterized forms are then developed for mass and stiffness matrices of n-noded elements (elements with n nodes with arbitrary arrangement). Optimization for the free parameters will deliver elements with better performance and less numerical dispersion error. Two of such elements are developed and compared for their ability in dispersion-error remission.