A triangular thin-shell finite element based on discrete Kirchhoff theory

Murthy, Sridhara S; Gallagher, Richard H.

doi:10.1016/0045-7825(86)90126-x

Cited by 27 publications

(10 citation statements)

References 12 publications

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“…The explicit expression of a V (z; z) depends on the shell formulation used in the structural problem, which will be derived as follows. The material derivative for the membrane-shear strain tensor can be obtained from its deÿnition in Equation (17) and from the formula in Equation (61) as In Equation (66), 1 ij (ż) implicitly depends on the design throughż and V 1 ij (z) represents the explicitly dependent part that can be computable from both the given analysis result z and the design velocity V. Similarly, the material derivative for the bending strain becomes…”

Section: Direct DI Erentiation Methodsmentioning

confidence: 99%

“…Unlike the Mindlin-Reissner plate formulation, the membrane and transverse shear strains are coupled in Equation (17). It is clear from the aforementioned assumptions that the structural energy form in Equation (14) is a quadratic function of the parametric co-ordinate .…”

Section: Variational Formulation For the Shell Structurementioning

confidence: 98%

“…This di culty is often referred to as shear and membrane locking. Many numerical schemes have been proposed to resolve numerical locking in FE-based approaches, including the selective reduced integration method [13], the B method [14], the mixed formulation [15], the assumed strain method [16], and the discrete Kirchho approach [17]. Several research results also have been reported in the plate=shell formulation by using the meshfree method.…”

Section: Introductionmentioning

confidence: 99%

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Meshfree analysis and design sensitivity analysis for shell structures

Kim

Choi

Chen

et al. 2002

Numerical Meth Engineering

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SUMMARYA uniÿed design sensitivity analysis method for a meshfree shell structure with respect to size, shape, and conÿguration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. Because of a strong connection to the CAD tool, the design variable is selected from the CAD parameters, and a consistent design velocity ÿeld is then computed by perturbing the surface geometric matrix. The material derivative concept is utilized in order to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and e ciency of the proposed design sensitivity analysis method compared to the analytical solution and the ÿnite di erence solution.

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Section: Direct DI Erentiation Methodsmentioning

confidence: 99%

Section: Variational Formulation For the Shell Structurementioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Meshfree analysis and design sensitivity analysis for shell structures

Kim

Choi

Chen

et al. 2002

Numerical Meth Engineering

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“…mad, Irons and Zienckiewicz [1] proposed shell elements in which the surface normals are interpolated separately from the surface geometry. This approach forms the basis for most currently used doubly curved shell elements, such as the one formulated by Murthy and Gallagher [14].…”

Section: Introductionmentioning

confidence: 99%

An efficient 3-D visualization technique for finite element models and other coarse volumes

Gallagher

Nagtegaal

1989

SIGGRAPH Comput. Graph.

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We have developed a technique that extends existing 3-D result visualization methods for use with discretized volumes such as finite element models, where result values are only available at coarsely spaced points throughout the volume. It represents results as smooth isosurfaces within the volume for one or more result values, using visually continuous, bi-cubic polynomials.At each of the points where results are available, result gradients are calculated by a finite difference procedure. The result values and result gradients are used to obtain the location of and the tangents to the isosurfaces on lines connecting the result points. Continuous doubly curved surfaces and surface normals are constructed separately between these discrete isosurface points using bi-cubic polynomials. The isosurfaces are rendered with standard light-source shading and optional levels of translucency, surrounded by translucent free faces of the structure.The method generates isosurfaces on an element-byelement basis, without reference at display time to the behavior of neighboring elements. It is intended for high speed display-time processing of either static or varying isosurface values.

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“…These elements, adapted for large rotation but small strain, provide accurate solutions in the framework of the classical (Kirchhoff) shell theory, where the shell normal remains perpendicular to the shell reference surface (i.e. negligible transverse shear) [17][18][19].…”

Section: Finite Element Modelmentioning

confidence: 99%

Experimental and numerical study on structural behavior of a single timber Textile Module

Sistaninia

Hudert

Humbert

et al. 2013

Engineering Structures

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. with different assembly conditions. The proposed geometrically nonlinear FE model allows evaluation of the stresses that are induced during the construction process and which may affect the structural integrity of the module. In particular, the risk of failure during assembly is identified using the anisotropic Tsai-Hill criterion.The structural behavior of the timber Textile Module is then investigated through bending tests using the constructed prototypes. During the loading procedure, the vertical deflections are measured at different locations on the prototype surface by means of external displacement transducers. Using the FE model, the corresponding deformed shapes are simulated by applying the bending loads on the prestressed Textile Module. Experimental displacements and FE predictions are thus compared and found to be in good agreement.

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A triangular thin-shell finite element based on discrete Kirchhoff theory

Cited by 27 publications

References 12 publications

Meshfree analysis and design sensitivity analysis for shell structures

Meshfree analysis and design sensitivity analysis for shell structures

An efficient 3-D visualization technique for finite element models and other coarse volumes

Experimental and numerical study on structural behavior of a single timber Textile Module

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