Modeling of Composite Shells in 6–Parameter Nonlinear Theory with Drilling Degree of Freedom

Chróścielewski, Jacek; Kreja, Ireneusz; Sabik, Agnieszka; Witkowski, Wojciech

doi:10.1080/15376494.2010.524972

Cited by 41 publications

(34 citation statements)

References 55 publications

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“…The load deflection curves are presented in Fig. 6, whereas Table 1 shows the [40,47,49]. Presented results, labeled as B6, are in good agreement with the reference solutions.…”

Section: Right-angle Cantileversupporting

confidence: 67%

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Structural response of existing spatial truss roof construction based on Cosserat rod theory

Miśkiewicz

2018

Continuum Mech. Thermodyn.

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Paper presents the application of the Cosserat rod theory and newly developed associated finite elements code as the tools that support in the expert-designing engineering practice. Mechanical principles of the 3D spatially curved rods, dynamics (statics) laws, principle of virtual work are discussed. Corresponding FEM approach with interpolation and accumulation techniques of state variables are shown that enable the formulation of the C 0 Lagrangian rod elements with 6-degrees of freedom per node. Two test examples are shown proving the correctness and suitability of the proposed formulation. Next, the developed FEM code is applied to assess the structural response of the spatial truss roof of the "Olivia" Sports Arena Gdansk, Poland. The numerical results are compared with load test results. It is shown that the proposed FEM approach yields correct results.

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“…The load deflection curves are presented in Fig. 6, whereas Table 1 shows the [40,47,49]. Presented results, labeled as B6, are in good agreement with the reference solutions.…”

Section: Right-angle Cantileversupporting

confidence: 67%

“…Hence, twostage interpolation originally proposed in [47] (compare with [48]) is employ indirect. The scheme is described in detail in [49] and references given there.…”

Section: Interpolation In So(3) Group Virtual Rotationsmentioning

confidence: 99%

Structural response of existing spatial truss roof construction based on Cosserat rod theory

Miśkiewicz

2018

Continuum Mech. Thermodyn.

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“…It should be noted that the rotation description methods are not unique and other rotation parameterizations, e.g., rotation tensor with canonical rotation vector update [24,25], are also feasible.…”

Section: Description Of Constrained Rotationmentioning

confidence: 99%

Weak form quadrature element analysis of geometrically exact shells

Zhang¹,

Zhong²

2015

International Journal of Non-Linear Mechanics

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“…Unfortunately, the former is sensitive to numerical ill conditioning in shallow shell geometry, whereas the latter is cumbersome in numerical implementation . To facilitate the modeling of nonsmooth shell structures, some researchers introduced the drilling rotation component in developing finite element formulations, leading to shell finite elements with three rotation parameters per node . Ibrahimbegovic and Frey proposed a consistent formulation of geometrically‐linear shell theory with drilling rotations by consistent linearization of geometrically nonlinear shell theory.…”

Section: Introductionmentioning

confidence: 99%

“…17 To facilitate the modeling of nonsmooth shell structures, some researchers introduced the drilling rotation component in developing finite element formulations, leading to shell finite elements with three rotation parameters per node. [17][18][19][20][21][22][23][24][25][26] Ibrahimbegovic and Frey [17][18][19] proposed a consistent formulation of geometrically-linear shell theory with drilling rotations by consistent linearization of geometrically nonlinear shell theory. Chroscielewski et al 20 proposed constitutive relations for composite shells within the framework of six-parameter shell theory with drilling degree of freedom.…”

Section: Introductionmentioning

confidence: 99%

A nine‐node corotational curved quadrilateral shell element for smooth, folded, and multishell structures

Vu‐Quoc

et al. 2018

Numerical Meth Engineering

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Summary A nine‐node corotational curved quadrilateral shell element with novel treatment for rotation at intersection of folded and multishell structures is presented. The element's corotational reference frame is defined by the two bisectors of the diagonal vectors generated using the four corner nodes and their cross product. In reference frame, the element rigid‐body rotations are excluded in calculating the local nodal variables from the global nodal variables. Rotations are not represented by axial (pseudo) vectors but by components of polar (proper) vectors, of which additivity and commutativity lead to symmetry of the tangent stiffness matrix. In the global coordinate system, the two smallest components of the midsurface normal vector at each node of a smooth shell or at nodes away from the intersection of nonsmooth shells are defined as rotational variables. In addition, of the two nodal orientation vectors at intersections of folded and multishell structures, two smallest components of one vector, together with one smaller component of another vector, are employed as rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure. In the local coordinate system, the two smallest components of the midsurface normal vector(s) at any node of a smooth shell or in each smooth patch of nonsmooth shell are defined as rotational variables. Different from other existing corotational finite‐element formulations, the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strain energy with respect to these nodal variables. To alleviate membrane and shear locking phenomena, the membrane strains and the out‐of‐plane shear strains are replaced with assumed strains, using the Mixed Interpolation of Tensorial Components approach, for obtaining the element tangent stiffness matrices and the internal force vector. Finally, a series of benchmark, challenging smooth, folded, and multishell structures undergoing large displacements and large rotations are analyzed to demonstrate the reliability and computational accuracy of the proposed formulation.

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Modeling of Composite Shells in 6–Parameter Nonlinear Theory with Drilling Degree of Freedom

Cited by 41 publications

References 55 publications

Structural response of existing spatial truss roof construction based on Cosserat rod theory

Structural response of existing spatial truss roof construction based on Cosserat rod theory

Weak form quadrature element analysis of geometrically exact shells

A nine‐node corotational curved quadrilateral shell element for smooth, folded, and multishell structures

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