Computer Methods in Applied Mechanics and Engineering 192 (2003) 975-1016. doi:10.1016/S0045-7825(02)00435-8Received by publisher: 2002-02-19Harvest Date: 2016-01-04 12:20:58DOI: 10.1016/S0045-7825(02)00435-8Page Range: 975-101

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SUMMARYWe present in this paper an efficient and accurate low-order solid-shell element formulation for analyses of large deformable multilayer shell structures with non-linear materials. The element has only displacement degrees of freedom (dofs), and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out-of-plane bending) and to remedy volumetric locking. Based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle, the in-plane and out-of-plane bending behaviours are improved and the locking associated with (nearly) incompressible materials is avoided via a new efficient enhancement of strain tensor. Shear locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. Two non-linear 3-D constitutive models (Mooney-Rivlin material and hyperelastoplastic material at finite strain) are applied directly without requiring the enforcement of the plane-stress assumption. In particular, we give a simple derivation for the hyperelastoplastic model using spectral representations. In addition, the present element has a well-defined lumped mass matrix, and provides double-side contact surfaces for shell contact problems. With the dynamics referred to a fixed inertial frame, the present element can be used to analyse multilayer shell structures undergoing large overall motion. Numerical examples involving static analyses and implicit/explicit dynamic analyses of multilayer shell structures with both material and geometric non-linearities are presented, and compared with existing results obtained from other shell elements and from a meshless method. It is shown that elements that did not pass the out-of-plane bending patch test could not provide accurate results, as compared to the present element formulation, which passed the out-of-plane bending patch test. The present element proves to be versatile and efficient in the modelling and analyses of general non-linear composite multilayer shell structures.

SUMMARYIn this paper, we present an optimal low-order accurate piezoelectric solid-shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out-of-plane bending). The combination of the present optimal piezoelectric solid-shell element and the optimal solid-shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3-D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid-shell element is further developed here. Based on the mixed Fraeijs de Veubeke-Hu-Washizu (FHW) variational principle, the in-plane and out-of-plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear-locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal-control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear-quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure.