Structural dynamic analysis using hybrid and mixed finite element models

This paper presents and discusses a hybrid-mixed stress finite element model for the dynamic analysis of structures, assuming a physically and geometrically linear behavior. In this model, both the stress and the displacement fields are approximated in the domain of each element. The displacements along the static boundary are also independently approximated. Orthonormal Legendre polynomials are used as approximation functions. The use of these functions enables the use of analytical closed form solutions for the computation of all structural operators and leads to the development of very effective p-refinement procedures. The linear dynamic analysis is performed using time integration procedures. For this purpose, the classical Newmark, Wilson-θ and α-HHT methods are implemented and tested. A recent and promising alternative approach, based on the definition of a mixed approximation in the time domain is also implemented and assessed. The model being discussed is applied to the solution of plane elasticity and Reissner–Mindlin plate bending problems. To validate the model, to illustrate its potential and to assess its accuracy and efficiency, several numerical examples are discussed and comparisons are made with analytical solutions and solutions provided by other numerical techniques.