In the present work, a shell finite element with a variable kinematic field based on a new zig-zag power function is proposed for the analysis of laminated shell structures. The kinematic field is written by using an arbitrary number of continuous piecewise polynomial functions. The polynomial expansion order of a generic subdomain is a combination of zig-zag power functions depending on the shell thickness coordinate. As in the classical layerwise approach, the shell thickness can be divided into a variable number of mathematical subdomains. The expansion order of each subdomain is an input parameter of the analysis. This feature enables the solution to be locally refined over generic regions of the shell thickness by enriching the kinematic field. The advanced finite shell elements with variable kinematics are formulated in the framework of the Carrera Unified Formulation. The finite element arrays are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modelling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on linear static stress analyses of composite laminated shell structures. The governing equations are obtained by applying the Principle of Virtual Displacements, and they are solved using the Finite Element method. Furthermore, the Mixed Interpolated Tensorial Components (MITC) method is employed to contrast the shear locking phenomenon. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present shell element.

Classical, higher-order, zig-zag and variable kinematic shell elements for the analysis of composite multilayered structures / Carrera, E.; Valvano, S.; Filippi, M.. - In: EUROPEAN JOURNAL OF MECHANICS. A, SOLIDS. - ISSN 0997-7538. - 72:(2018), pp. 97-110. [10.1016/j.euromechsol.2018.04.015]

### Classical, higher-order, zig-zag and variable kinematic shell elements for the analysis of composite multilayered structures

#### Abstract

In the present work, a shell finite element with a variable kinematic field based on a new zig-zag power function is proposed for the analysis of laminated shell structures. The kinematic field is written by using an arbitrary number of continuous piecewise polynomial functions. The polynomial expansion order of a generic subdomain is a combination of zig-zag power functions depending on the shell thickness coordinate. As in the classical layerwise approach, the shell thickness can be divided into a variable number of mathematical subdomains. The expansion order of each subdomain is an input parameter of the analysis. This feature enables the solution to be locally refined over generic regions of the shell thickness by enriching the kinematic field. The advanced finite shell elements with variable kinematics are formulated in the framework of the Carrera Unified Formulation. The finite element arrays are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modelling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on linear static stress analyses of composite laminated shell structures. The governing equations are obtained by applying the Principle of Virtual Displacements, and they are solved using the Finite Element method. Furthermore, the Mixed Interpolated Tensorial Components (MITC) method is employed to contrast the shear locking phenomenon. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present shell element.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2722201`