(Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams)

Francesco Tornabene

© 2013-2024 University of Salento

DiQuMASPAB is an acronym for Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams. The purpose of this software is to provide a general framework for modelling complex structures such as moderately thick doubly-curved shells and plates, using the Generalized Differential Quadrature (GDQ) method. DiQuMASPAB project is one of the activities of CIMEST Research Centre. This code allows the user to investigate the static and dynamic analyses of doubly-curved, singly-curved laminated composite and functionally graded (FGM) shells, panels and degenerate plates.

To the best knowledge of the authors, there are three different ways to study anisotropic shell structures: the 3D Elasticity, Equivalent-Single-Layer (ESL) and Layer-Wise (LW) theories. A 2D generalized displacement field suitable to represent in a unified form most of the kinematical hypothesis presented in literature is implemented in DiQuMASPAB software. The mechanical model used is based on the Unified Formulation (UF) with curvature effect included for the ESL and LW approaches. The zig-zag effect is also considered in the ESL theory using the Murakami function. Various shear functions through the thickness of the shell structure can be chosen, combined and compared with each other by the user in order to study different types of higher-order theories.

The theoretical implementation of these theories leads to an explicit form of the Fundamental Nuclei (FN) for laminated completely doubly-curved shells. The FN can be used not only for the ESL approach, but also for the LW theory. Concerning a laminated composite doubly-curved shell in orthogonal curvilinear coordinate system, the fundamental operators are explicitly obtained for the first time by the authors. Thanks to the generality of the developed CUF approach, the general theoretical formulation of 2D Higher-order Shear Deformation Theory (HSDT) for doubly-curved shells can also be computed, as well as the classical First-order and Third-order Shear Deformation Theories. DiQuMASPAB software allows to consider up to 24 degrees of freedom for the ESL theory and up to 18 degrees of freedom for each layer when the LW theory is selected.

To define the arbitrary shape of the middle surface of shells and panels with different curvatures, the Differential Geometry theory is used coupled with GDQ technique. The GDQ rule permits to numerically evaluate all the derivatives required for describing the geometry of doubly-curved shell structures.

The shell governing equations are expressed as functions of various kinematic parameters, when the constitutive and the kinematic relationships are known. The system of second-order linear partial differential equations is solved using the GDQ approach.

A three-dimensional stress recovery procedure based on the 3D Elasticity equations in orthogonal curvilinear coordinate system for doubly-curved shells and panels is also used to reconstruct all the stresses and strains through the thickness of the shell structure.and to satisfy the top and bottom boundary conditions of the laminated composite shell or panel. The numerical procedure related to the stress and strain recovery is solved using the GDQ technique. All displacements, strains and stresses can be plotted through the thickness of the selected shell structure. Several lamination schemes, FGM distributions through the thickness, loadings and boundary conditions can be considered. Moreover, DiQuMASPAB software has an embedded tool for the comparison with throught-the-thickness plots obtained with numerical solutions of different codes.

The theoretical implementation of the present software has been performed following the mathematical background presented in the books:

We are looking forward to receiving your feedbacks about our project. Please, contact us.


If you plan to use DiQuMASPAB software, please cite it as follows:

F. Tornabene, DiQuMASPAB Software, DII Department, University of Salento (https://www.diqumaspab.it)

*contact: Francesco Tornabene