Geometrically exact sandwich shells: The dynamic case

Vu‐Quoc, L.; Deng, Huachao; Tan, X.G.

doi:10.1016/s0045-7825(00)00181-x

Cited by 39 publications

(10 citation statements)

References 23 publications

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“…Consequently, a form similar to Equation (27) can be established for the variational quantities in Equation (24). Assembling the above matrix operators together, we write…”

Section: Finite Element Discretizationmentioning

confidence: 99%

Inverse formulation for geometrically exact stress resultant shells

Zhou

2007

Numerical Meth Engineering

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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.

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“…Consequently, a form similar to Equation (27) can be established for the variational quantities in Equation (24). Assembling the above matrix operators together, we write…”

Section: Finite Element Discretizationmentioning

confidence: 99%

Inverse formulation for geometrically exact stress resultant shells

Zhou

2007

Numerical Meth Engineering

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“…Within the frameworks of¯rst-order shear deformation laminated theories, Kim et al 9 presented a 4-node co-rotational composite shell element combining an enhanced assumed strain in the membrane strains and assumed natural strains in the shear strains; Auricchio and Sacco 15 obtained a 4-node¯nite element for the analysis of laminated composite plates through a mixed-enhanced approach; Chun et al 16 proposed a 4-node laminated shell element with drilling degrees of freedom, where assumed stress and enhanced strain techniques are adopted to prevent locking problems; Daghia et al 17 developed a quadrilateral 4-node¯nite element from a hybrid stress formulation involving compatible displacements and element-wise equilibrated stress resultants as primary variables; Vu-Quoc et al [18][19][20] developed a class of geometrically-exact multilayer shell formulation that can account for large deformation and large overall motion.…”

Section: Introductionmentioning

confidence: 99%

A 4-Node Co-Rotational Quadrilateral Composite Shell Element

Zheng

Vu‐Quoc

et al. 2016

Int. J. Str. Stab. Dyn.

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A 4-node co-rotational quadrilateral composite shell element is presented. The local coordinate system of the element is a co-rotational framework defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product. Thus, the element rigid-body rotations are excluded in calculating the local nodal variables from the global nodal variables. Compared with other existing co-rotational finite-element formulations, the present element has two features: (i) The two smallest components of the mid-surface normal vector at each node are defined as the rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure; (ii) both element tangent stiffness matrices in the local and global coordinate systems are symmetric owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation with respect to the global nodal variables. In the modeling of composite structures, the first-order shear deformable laminated plate theory is adopted in the local element formulation, where both the thickness deformation and the normal stress in the direction of the shell thickness are ignored, and an assumed strain method is employed to alleviate the membrane and shear locking phenomena. Several examples involving composite plates and shells with large displacements and large rotations are presented to testify to the reliability and convergence of the present formulation

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“…A few studies considered fully large deformation [49,50]. In this work, a straindisplacement relations for large deflection, large inplane strains and small rotations, so-called Green strain tensor with small rotations, is proposed.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric analysis for flexural behavior of composite plates considering large deformation with small rotations

Le-Manh

Luu-Anh

Lee

2015

Mechanics of Advanced Materials and Structures

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A large deformation theory, so-called Green strains with small rotations, is proposed and employed for flexural analysis of composite plates. Isogeometric analysis cooperated with firstorder shear deformation theory is used to derive finite element models. Strain-displacement relations in sense of von-Karman theory and the proposed theory are formulated. Shear locking phenomenon is avoided by using reduced integration technique. Newton-Raphson method is employed for nonlinear analysis procedure. Numerical examples including isotropic and laminated composite plates under different boundary conditions are investigated. The results have been verified with those available in literature and show the advantages of the proposed strain theory.

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Geometrically exact sandwich shells: The dynamic case

Cited by 39 publications

References 23 publications

Inverse formulation for geometrically exact stress resultant shells

Inverse formulation for geometrically exact stress resultant shells

A 4-Node Co-Rotational Quadrilateral Composite Shell Element

Isogeometric analysis for flexural behavior of composite plates considering large deformation with small rotations

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