A finite element approach to statical and dynamical analysis of geometrically nonlinear structures

A geometrically nonlinear formulation to analyse structures in the hypotheses of large displacements and rotations and small strains is presented. In this formulation, applied to low-order elements and based on the total Lagrangian kinematics, the use of the rotation matrices is bypassed. 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 element reference system independent. In addition, complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. Numerical tests have been carried out to validate the developed technique both in the statical and in the dynamical context. (C) 2010 Elsevier B.V. All rights reserved.