FEM analysis of Cosserat plates and shells based on some constitutive relations

We carry out further study of the constitutive laws for Cosserat plates developed by Altenbach and Eremeyev. In particular, we examine the problem of choice of the micropolar material coefficients. Requiring that the constitutive matrix is positive definite, we establish some bounds on values of micropolar constants. The constitutive relations for Cosserat plates have been implemented into formulation of shell finite elements developed within the framework of the statically and kinematically exact, nonlinear six‐parameter shell theory. By the linear parametric‐sensitivity analysis we study the influence of the micropolar material constants on the response of shell structure with orthogonal intersections of branches. Such structures can naturally be analyzed using the six‐parameter shell theory. Having established the most influential coefficients, we show how these values affect the behavior of the structure in the nonlinear range of deformations. The authors carry out further study of the constitutive laws for Cosserat plates developed by Altenbach and Eremeyev. In particular, they examine the problem of choice of the micropolar material coefficients. Requiring that the constitutive matrix is positive definite, they establish some bounds on values of micropolar constants. The constitutive relations for Cosserat plates have been implemented into formulation of shell finite elements developed within the framework of the statically and kinematically exact, nonlinear six‐parameter shell theory. By the linear parametric‐sensitivity analysis the authors study the influence of the micropolar material constants on the response of shell structure with orthogonal intersections of branches.