김경종
79 lines
3.6 KiB
Markdown
79 lines
3.6 KiB
Markdown
---
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type: source
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title: "A Continuum Mechanics Based Four-Node Shell Element for General Non-Linear Analysis"
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source_type: paper
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authors:
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- "Eduardo N. Dvorkin"
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- "Klaus-Jurgen Bathe"
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date_received: 1983-12
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aliases:
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- AContinuumMechanicsBasedFourNodeShell
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- four-node shell element paper
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- Dvorkin Bathe four-node shell
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created: 2026-05-28
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updated: 2026-05-28
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address: c-000017
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tags:
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- source
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- finite-element-method
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- shell-elements
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- nonlinear-analysis
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status: current
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confidence: high
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raw_path: ".raw/AContinuumMechanicsBasedFourNodeShell/"
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source_files:
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markdown_files: 2
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image_files: 100
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related:
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- "[[Eduardo N. Dvorkin]]"
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- "[[Klaus-Jurgen Bathe]]"
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- "[[Continuum Mechanics Based Four-Node Shell Element]]"
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- "[[Assumed Transverse Shear Strain Interpolation]]"
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- "[[Total Lagrangian Shell Formulation]]"
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- "[[Nonlinear Finite Element Analysis]]"
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- "[[Isoparametric Finite Elements]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC4 Shell Element]]"
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---
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# A Continuum Mechanics Based Four-Node Shell Element for General Non-Linear Analysis
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## Summary
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This paper presents a four-node non-flat quadrilateral shell element for general nonlinear analysis. The element is formulated from three-dimensional continuum mechanics instead of a specialized shell theory, and is intended for thin and thick shells, arbitrary shell geometries, large displacement and rotation response with small strains, and material nonlinear behavior.
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The local source is a converted Markdown/image extraction of the paper: two Markdown files and 100 extracted images under `.raw/AContinuumMechanicsBasedFourNodeShell/`.
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## Key Contributions
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- The element uses a continuum-mechanics description with convected coordinates, so shell behavior is derived from the three-dimensional virtual work statement.
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- The formulation separates transverse shear strain interpolation from the standard displacement interpolation to avoid shear locking in thin shell bending.
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- The paper develops a total Lagrangian nonlinear formulation for large displacements and rotations with small strains.
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- The numerical tests cover rigid-body modes, thin-shell bending, distorted meshes, cylindrical shells, pinched cylinders, large-deflection cantilevers, shallow spherical shell snap-through behavior, stiffened plate buckling, and elastoplastic circular plate response.
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- The authors report no spurious zero-energy modes with full numerical integration in the tested cases.
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## Concepts Introduced
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- [[Continuum Mechanics Based Four-Node Shell Element]]
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- [[Assumed Transverse Shear Strain Interpolation]]
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- [[Total Lagrangian Shell Formulation]]
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## Links To Existing Wiki
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- [[Isoparametric Finite Elements]] supplies the geometry mapping and quadrature machinery used by the shell element.
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- [[Mixed Finite Element Formulations]] gives context for constraint-aware interpolation choices that prevent locking.
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- [[Nonlinear Finite Element Analysis]] gives the broader incremental equilibrium setting for the element's large-displacement examples.
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- [[Finite Element Method]] is the parent discretization framework.
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- [[Four-Node-Quadrilateral-Shell-Element-MITC4|Four-Node Quadrilateral Shell Element MITC4]] is a later implementation-focused source that follows the same four-node shell lineage and emphasizes the MITC locking remedy.
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## Entities Mentioned
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- [[Eduardo N. Dvorkin]]
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- [[Klaus-Jurgen Bathe]]
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## Source Notes
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- Source path: `.raw/AContinuumMechanicsBasedFourNodeShell/`
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- Composite source hash recorded in `.raw/.manifest.json`.
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- The source extraction contains encoding artifacts in names and symbols. Derived wiki pages normalize `Klaus-Jurgen Bathe` to the existing vault spelling.
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