Spring lattice models in the nonlinear analysis of membrane shells – An applicability study in elasticity, plasticity and damage. (March 2020) - Doltsinis, Ioannis; Reck, Michael; Dias da Silva, Vitor
Highlights: Nonlinear analysis of membrane shells by three distinct spring cell models. Stiffness-, flexibility-, and complete substitutes of the finite element triangle. Substantially large deformations in elasticity, plasticity, visco-plastic damage. Comparison with the finite element solutions and discussion on performance. Remarks on stress and strain representation, mesh dependency and nonlinearity. Abstract: Following the accomplishment of fundamental research on- and the development of improved spring models, this work investigates the utility of spring lattice models in representing actual structures. The study explores the applicability of spring lattice models for the analysis of nonlinear shell structures. Of importance the limits of the approximation of defective bar-spring models, on the one hand, and the attempt of a rigorous representation of the continuum by introducing additional spring elements, on the other hand. Preliminary investigations indicate appropriateness for membrane shells, but reveal weakness in modelling shells with bending stiffness by axial bar elements despite three-dimensional cell arrangements. Therefore the focus here is on membrane structures. A direct insight to the employed triangular spring cells is offered by the approach based on the natural description of the continuum suiting the individual geometry. The investigations address specifically the performance of the spring models when applied to problems involving geometrical and material non-linearity. For this purpose the spring models have been tested against the continuum finite element distinctly in elasticity and in plasticity in the context of large deformations. In addition, the effect of damage is simulated by means of a regularized constitutive model of softening plasticity.