Geometrically-exact sandwich shells: The static case

Vu‐Quoc, L.; Deng, Huachao; Tan, X.G.

doi:10.1016/s0045-7825(99)00294-7

Cited by 39 publications

(19 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The kinematic description of the present element consists of only displacement dofs at the top and bottom surfaces of the shell. Complex finite rotation updates such as those found in stress-resultant shell elements [9] is avoided. The present formulation also provides a natural way to connect to regular solid elements (see Figure 1) without the need for transition elements or submodelling technique as in Reference [8], in which the modelling processes are laborious and error prone.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient and accurate multilayer solid-shell element: non-linear materials at finite strain

Tan

Vu‐Quoc

2005

Int. J. Numer. Meth. Engng

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

“…To obtain the same performance in bending as with stress-resultant shell formulations with plane-stress assumption (e.g. Reference [9]), the enhanced assumed strain (EAS) method and the assumed natural strain (ANS) method are employed in the present solid-shell formulation.…”

Section: Introductionmentioning

confidence: 99%

Efficient and accurate multilayer solid-shell element: non-linear materials at finite strain

Tan

Vu‐Quoc

2005

Int. J. Numer. Meth. Engng

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the relevant literature, [Simo and Fox 1989;VuQuoc et al 2000], membranal, curvature and shear strains for the shell have been defined as:…”

Section: Shear Deformable and Polar Shell Modelsmentioning

confidence: 99%

Nonlinear shell theory: a duality approach

Romano

Sellitto

Barretta

2007

JOMMS

View full text Add to dashboard Cite

The nonlinear kinematics of thin shells is developed in full generality according to a duality approach in which kinematics plays the basic role in the definition of the model. The Kirchhoff-Love shell model is the central issue and is discussed in detail but shear deformable and polar models are also considered and critically reviewed. The analysis is developed with a coordinate-free approach which provides a direct geometrical picture of the shell model. The finite and tangent Green strains of the foliated continuum are explicitly expressed in terms of middle surface kinematics. The new expressions contributed here do not require the splitting of the velocity into parallel and normal components to the middle surface, and provide a computationally convenient context. Finite strain measures for the shell and their tangent and secant rates are analyzed and consistency and nonredundancy properties are discussed. The relations between the finite Green strain, its tangent and secant rates and the corresponding shell strains, are provided. The differential and boundary equilibrium equations of the shell are given in variational terms, both in unsplit and split form. A new expression of the boundary equilibrium equations is contributed and its mechanical soundness with respect to the classical one is emphasized. Equilibrium in a reference placement for the shell model is briefly discussed.

show abstract

“…Nevertheless, the discretization through the thickness direction should be similar with the mesh density in the in-plane direction due to the limitation of the element aspect ratio, resulting in much higher computational cost since the overall model composed of great many solid elements comprises million degrees of freedom. In contrast, the shell elements are computationally efficient [9][10][11], but most of shell elements are not able to accurately capture the interlaminar transverse shear stress and the transverse normal stress through the plate thickness direction, because these shell elements employ the common kinematic assumptions of inextensibility in the thickness direction or the zero transverse normal-stress condition etc.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Shi

Wang

2017

Curved and Layered Structures

View full text Add to dashboard Cite

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.

show abstract

Geometrically-exact sandwich shells: The static case

Abstract: Computer Methods in Applied Mechanics and Engineering 189 (2000) 167-203. doi:10.1016/S0045-7825(99)00294-7Received by publisher: 1998-06-25Harvest Date: 2016-01-04 12:20:58DOI: 10.1016/S0045-7825(99)00294-7Page Range: 167-20

Cited by 39 publications

References 14 publications

Efficient and accurate multilayer solid-shell element: non-linear materials at finite strain

Efficient and accurate multilayer solid-shell element: non-linear materials at finite strain

Nonlinear shell theory: a duality approach

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

Contact Info

Product

Resources

About