A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Discrete Kirchhoff–Love shell quadrilateral finite element designed from cubic Hermite edge curves and Coons surface patch
https://orcid.org/0000-0003-2858-8726
https://orcid.org/0000-0001-8249-3387
Abstract We present a nonlinear discrete Kirchhoff–Love four-node shell finite element that is based on the cubic Hermite edge curves and the bilinear Coons surface patch spanning the surface between them. The cubic Hermite edge curves are constructed by minimizing the bending curvature of a spatial curve connecting two adjacent nodes of the element. The -continuity is obtained at each node of the finite element mesh. Namely, the tangent vectors of the set of the edge curves attached to a given node of the mesh share the same tangent plane to the shell mid-surface for any configuration. To avoid the membrane locking, common in shell elements with higher-order interpolations, the assumed natural strains are adopted, solving the plate compatibility equation. The derived element has 5 degrees of freedom per node, 3 mid-surface displacements and 2 rotations of the mid-surface normal vector, which also rotate the corresponding mid-surface tangent plane. Several numerical examples illustrate its performance in linear and nonlinear tests, for both regular and distorted meshes.
Highlights Discrete Kirchhoff–Love nonlinear shell element with G−1-continuity at nodes is developed. Coons surface patch is used for approximation of the shell-mid-surface. Hermite edge curves are obtained by minimizing the bending energy of spatial curve.
Discrete Kirchhoff–Love shell quadrilateral finite element designed from cubic Hermite edge curves and Coons surface patch
https://orcid.org/0000-0003-2858-8726
https://orcid.org/0000-0001-8249-3387
Abstract We present a nonlinear discrete Kirchhoff–Love four-node shell finite element that is based on the cubic Hermite edge curves and the bilinear Coons surface patch spanning the surface between them. The cubic Hermite edge curves are constructed by minimizing the bending curvature of a spatial curve connecting two adjacent nodes of the element. The -continuity is obtained at each node of the finite element mesh. Namely, the tangent vectors of the set of the edge curves attached to a given node of the mesh share the same tangent plane to the shell mid-surface for any configuration. To avoid the membrane locking, common in shell elements with higher-order interpolations, the assumed natural strains are adopted, solving the plate compatibility equation. The derived element has 5 degrees of freedom per node, 3 mid-surface displacements and 2 rotations of the mid-surface normal vector, which also rotate the corresponding mid-surface tangent plane. Several numerical examples illustrate its performance in linear and nonlinear tests, for both regular and distorted meshes.
Highlights Discrete Kirchhoff–Love nonlinear shell element with G−1-continuity at nodes is developed. Coons surface patch is used for approximation of the shell-mid-surface. Hermite edge curves are obtained by minimizing the bending energy of spatial curve.
Discrete Kirchhoff–Love shell quadrilateral finite element designed from cubic Hermite edge curves and Coons surface patch
https://orcid.org/0000-0003-2858-8726
https://orcid.org/0000-0001-8249-3387
Abstract We present a nonlinear discrete Kirchhoff–Love four-node shell finite element that is based on the cubic Hermite edge curves and the bilinear Coons surface patch spanning the surface between them. The cubic Hermite edge curves are constructed by minimizing the bending curvature of a spatial curve connecting two adjacent nodes of the element. The -continuity is obtained at each node of the finite element mesh. Namely, the tangent vectors of the set of the edge curves attached to a given node of the mesh share the same tangent plane to the shell mid-surface for any configuration. To avoid the membrane locking, common in shell elements with higher-order interpolations, the assumed natural strains are adopted, solving the plate compatibility equation. The derived element has 5 degrees of freedom per node, 3 mid-surface displacements and 2 rotations of the mid-surface normal vector, which also rotate the corresponding mid-surface tangent plane. Several numerical examples illustrate its performance in linear and nonlinear tests, for both regular and distorted meshes.
Highlights Discrete Kirchhoff–Love nonlinear shell element with G−1-continuity at nodes is developed. Coons surface patch is used for approximation of the shell-mid-surface. Hermite edge curves are obtained by minimizing the bending energy of spatial curve.
Discrete Kirchhoff–Love shell quadrilateral finite element designed from cubic Hermite edge curves and Coons surface patch
Veldin, Tomo (author) / Brank, Boštjan (author) / Brojan, Miha (author)
Thin-Walled Structures ; 168
2021-08-05
Article (Journal)
Electronic Resource
English
A Cubic Strain Quadrilateral Finite Element
| British Library Online Contents | 1996
A Curved Quadrilateral Kirchhoff Plate Bending Element
| British Library Online Contents | 2001
A new discrete Kirchhoff quadrilateral element based on the third-order theory for composite plates
| British Library Online Contents | 2007
Asymmetric quadrilateral shell elements for finite strains
| British Library Online Contents | 2013
An application of Coons patch to generate grid-based digital elevation models
| Online Contents | 2011