M. D'Ottavio

Variable-Kinematics Approach for Linearized Buckling Analysis of Laminated Plates and Shells

This work deals with the linearized buckling analysis of laminated plates and shells. A variable-kinematics approach with hierarchical capabilities is considered to establish the accuracy of a large variety of classical and advanced plate/shell theories in order to evaluate buckling loads. So-called equivalent-single-layer as well as layerwise-variable descriptions are implemented. Interlaminar continuity of transverse shear and normal stresses are a priori fulfilled by referring to Reissners mixed variational theorem. Stability equations are derived in compact form by referring to Carreras unified formulation for the most general case of doubly curved shells. The eigenvalue problem is solved in the case of closed-form solutions related to simply supported boundary conditions and axially loaded multilayered plates/shells made of orthotropic layers. The casesofaxial constant strains and constant stresses are considered and compared to available three-dimensional and two-dimensional results. Results related to Love and Donnell approximations are implemented for comparison purposes. The accuracy of various approximations is established for significant multilayered plate and shell problems.

An Efficient Finite Shell Element for the Static Response of Piezoelectric Laminates

This study presents a novel finite element (FE) for shell structures including piezoelectric actuators and sensors. Based on a conventional 8-node shell formulation and the classical displacement-based variational formulation, the present element has an enriched description of the transverse kinematics in order to consistently retain the full three-dimensional (3D) piezoelectric coupling. Furthermore, a layer-wise description of the electric degrees of freedom permits to account for embedded piezoelectric actuators and sensors. The robustness of the FE is enhanced by referring to an established technique that avoids transverse shear locking and membrane locking. Numerical results are given which validate the present implementation and highlight the efficiency and accuracy of the proposed formulation. Additionally, some new reference solutions for the static behavior of piezoelectric shells are provided by means of 3D FE computations with a commercial software.

Assessment of free-edge singularities in composite laminates using higher-order plate elements

Abstract The capabilities and limitations of refined two-dimensional (2D) composite plate elements are discussed with respect to the stress concentration problem occurring at traction-free edges. Classical displacement-based and advanced partially mixed finite elements are formulated according to Carrera’s Unified Formulation (CUF). Rectangular laminates are analyzed under extension and bending loading, where the attention is focused on the local stress response at the free edges. Present results are compared with reference results available in the literature and a 3D finite element model. A power law representation for a singular stress field is used to fit the obtained stresses in the vicinity of the free edge, and the parameters are used to assess the CUF elements and to compare the free-edge effect occurring in extension and bending.

Sensitivity Analysis of Thickness Assumptions for Piezoelectric Plate Models

This article compares different axiomatic 2D theories for linear homogeneous piezoelectric plates. Simple actuator and sensor configurations are considered of thin and thick piezoelectric ceramics working either in transverse extension (31 mode) or in shear mode (15 mode). By generalizing a previously established unified formulation, a large number of different through-thickness approximations for the in-plane displacement, the transverse displacement and the electrostatic potential are introduced. Additionally, either full 3D constitutive law or reduced constitutive equations accounting for a vanishing transverse normal stress are employed in these plate theories. By referring to an analytical Naviertype closed-form solution, a systematic assessment of various 2D models is performed. The proposed sensitivity analysis of plate theories with respect to their electromechanical response can serve as a useful guide for choosing appropriate models depending on the piezoelectric polarization scheme, the use as sensor or actuator, and the plate thickness.

Classical, first order, and advanced theories

Abstract This chapter is dedicated to theories for the mechanical analysis of structures. An overview of the literature is given based on classical and advanced theories. A general classification is first introduced concerning displacement or mixed models, asymptotic or axiomatic approaches, and equivalent single-layer or layerwise modeling techniques. The proposed classification pertains to beam, plate, and shell models. Classical theories and advanced ones are subsequently presented with precise description of the underlying hypotheses. For the sake of conciseness, the mathematical description is limited to plate structures and beam theories are briefly discussed in the Appendix. Some numerical results are given for layered and sandwich structures with respect to linear bending, free vibration, and buckling analyses. The model assessment allows to define applicability ranges and limitations of these theories.