Abstract
Most of mechanical systems and complex structures exhibit plate and shell components. Therefore, 2D simulation, based on plate and shell theory, appears as an appealing choice in structural analysis as it allows reducing the computational complexity. Nevertheless, this 2D framework fails for capturing rich physics compromising the usual hypotheses considered when deriving standard plate and shell theories. To circumvent, or at least alleviate this issue, authors proposed in their former works an in-plane–out-of-plane separated representation able to capture rich 3D behaviors while keeping the computational complexity the one of 2D simulations. In the present paper we propose an efficient integration of fully 3D descriptions into existing plate software.
Highlights
We consider the linear elastostatic problem defined in the plate domain = xy × z, with xy = [0, Hx] × [0, Hy] and z = [0, Hz] in which the thickness dimension is much lower than the other ones, i.e. Hz Hx, Hy.The linear elastic behavior relating the Cauchy’s stress σ and the strain ε using Voigt notation reads σ = C ε, (1)where C is the elasticity matrix
Remark 2 the in-plane functions determining the kinematics can be obtained from a standard plate theory software by using the elementary rigidity and forces given respectively by Kxey and Bexy considered in expression (26) and (38)
As in the considered domain the thickness dimension is not much lower than the other ones, the linear variation of the displacement field along the thickness described by (2) is not more true as we can notice in Fig. 2 that compares the plate solution from the fully 3D solution assumed as reference
Summary
For the sake of generality we are considering generic functions f x(z), f y(z) and f z(z) assumed known, but than can be different to the ones related to the standard Reissner– Mindlin plate theory, and its associated 3D kinematics given by Eq (12). If we assume an approximation based on a piecewise linear interpolation on a triangular finite element, related to an in-plane mesh of xy = ∪Ee=1 functions defined by Nie(x, y), i = 1, 2, 3; e = 1, .
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