Structural dynamical analysis by a lengths-based description of the small strains in the finite displacements regime

Abstract

In this work we present a geometrically nonlinear formulation to analyze the motion of structures in the case of large displacements and rotations and small strains. In this formulation, applied to low-order elements and based on the total Lagrangian kinematic description, the use of the rotation matrices is bypassed. In this way a selective based definition of the strain tensor, used in order to avoid shear-locking problems, is effected by the linear definition of deformations because it is independent of element reference system. In addition, complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. Numerical tests have been carried out to evaluate the validity of the developed method.