Multilayer shells: Geometrically-exact formulation of equations of motion

Shi

Curved and Layered Structures

2017

This paper presents the efficient modeling and analysis of laminated composite plates using an eightnode quasi-conforming solid-shell element, named as QCSS8. The present element QCSS8 is not only lockingfree, but highly computational efficiency as it possesses the explicit element stiffness matrix. All the six components of stresses can be evaluated directly by QCSS8 in terms of the 3-D constitutive equations and the appropriately assumed element strain field. Several typical numerical examples of laminated plates are solved to validate QCSS8, and the resulting values are compared with analytical solutions and the numerical results of solid/solidshell elements of commercial codes computed by the present authors in which fine meshes were used. The numerical results show that QCSS8 can give accurate displacements and stresses of laminated composite plates even with coarse meshes. Furthermore, QCSS8 yields also accurate transverse normal strain which is very important for the evaluation of interlaminar stresses in laminated plates. Since each lamina of laminated composite plates can be modeled naturally by one or a few layers of solidshell elements and a large aspect ratio of element edge to thickness is allowed in solid-shell elements, the present solid-shell element QCSS8 is extremely appropriate for the modeling of laminated composite plates.

Section: The Element Assumed Strain Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Displacement and stress analysis of laminated composite plates using an eight-node quasi-conforming solid-shell element

Shi

Curved and Layered Structures

2017

Numerical Meth Engineering

“…Similarly, for the coordinate surface 2 = const, Vu-Quoc et al [21,22] employed the vectors {N } and {M } as the resultant variables. In terms of these variables, the equations of motion take a simpler form, as seen from Equation (84) in [21] and Equation (127) in [22].…”

Section: Mechanics Of Geometrically Exact Shellsmentioning

confidence: 99%

“…In terms of these variables, the equations of motion take a simpler form, as seen from Equation (84) in [21] and Equation (127) in [22].…”

Section: Mechanics Of Geometrically Exact Shellsmentioning

confidence: 99%

Inverse formulation for geometrically exact stress resultant shells

Zhou

2007

SUMMARYThe inverse elastostatic method deals with a class of problems in which a deformed configuration of an elastic body is known while the initial stress-free configuration or the stress in the deformed state is to be determined. The method is imperative for certain problems in engineering applications. Computational methods of inverse elastostatics have been established for elastic continua. In this paper, we present an inverse method for thin-wall structures modeled as geometrically exact stress resultant shells. The theoretical basis and the details of implementation are discussed. Numerical examples involving both isotopic and anisotropic materials are presented. The practical utility of the method is demonstrated using an example of human aneurysm stress analysis.

Numerical Meth Engineering

“…Theoretical research for treating laminated thin structures has been widely developed (e.g., [1][2][3][4][5]). Depending on theories of laminated plates and shells, these methods are mainly valid for classical multilayer structures and do not account for complex multiphase morphologies.…”

Section: Introductionmentioning

confidence: 99%

Multiscale computational homogenization of heterogeneous shells at small strains with extensions to finite displacements and buckling

Nezamabadi

Zahrouni

et al. 2015

To cite this version:Yu Cong, Saeid Nezamabadi, Hamid Zahrouni, Julien Yvonnet. Multiscale computational homogenization of heterogeneous shells at small strains with extensions to finite displacements and buckling. International Journal for Numerical Methods in Engineering, Wiley, 2015, 104 (4) SUMMARYIn this paper, a framework for computational homogenization of shell structures is proposed in the context of small-strain elastostatics, with extensions to large displacements and large rotations. At the macroscopic scale, heterogeneous thin structures are modeled using a homogenized shell model, based on a versatile three-dimensional seven-parameter shell formulation, incorporating a through-thickness and pre-integrated constitutive relationship. In the context of small strains, we show that the local solution on the elementary cell can be decomposed into six strains and six-strain gradient modes, associated with corresponding boundary conditions. The heterogeneities can have arbitrary morphology but are assumed to be periodically distributed in the tangential direction of the shell. We then propose an extension of the small-strain framework to geometrical nonlinearities. The procedure is purely sequential and does not involve coupling between scales. The homogenization method is validated and illustrated through examples involving large displacements and buckling of heterogeneous plates and shells.