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A heuristic viscosity-type dissipation of strains is applied for controlling high frequency oscillation damping in a one-step time integration. The basic idea of the approach is to apply damping in locations, where it is needed, at times when it is needed. To this end a computationally efficient algorithm for identifying the need for damping is developed. The identification algorithm keeps track of the number of recent changes of signs of strain increments, which helps in decision whether damping should be engaged or not. A special scaling function is introduced to smoothen the transition between the damped and undamped phases. The approach is verified in the analysis of the geometrically exact plane elastic beam. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the equations of the linearized geometrically exact three-dimensional beam theory of naturally curved and twisted beams. A new finite-element formulation for the linearized theory is proposed in which the strain vectors are the only unknown functions. The linear form of the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. An arbitrary curved and twisted axis of the beam is taken into account which demands proper consideration of the non-linearity of spatial rotations. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by comparing present numerical results with various analytical and numerical results. [Copyright &y& Elsevier]

Abstract: This paper introduces a new finite element formulation of the ‘geometrically exact finite-strain beam theory’. The formulation employs the generalized virtual work principle. In the resulting governing equations of the beam, the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples. [Copyright &y& Elsevier]