김경종
73 lines
3.8 KiB
Markdown
73 lines
3.8 KiB
Markdown
---
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type: concept
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title: "Continuum Mechanics Based Four-Node Shell Element"
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complexity: advanced
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domain: computational-mechanics
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aliases:
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- four-node shell element
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- Dvorkin-Bathe shell element
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- continuum mechanics shell element
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created: 2026-05-28
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updated: 2026-05-28
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address: c-000019
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tags:
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- concept
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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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related:
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[Basic Shell Mathematical Model]]"
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- "[[Shell Locking Phenomenon]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC4 Shell Element]]"
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- "[[Scordelis-Lo Shell Benchmark]]"
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- "[[Assumed Transverse Shear Strain Interpolation]]"
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- "[[Total Lagrangian Shell Formulation]]"
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- "[[Isoparametric Finite Elements]]"
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- "[[Nonlinear Finite Element Analysis]]"
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sources:
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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---
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# Continuum Mechanics Based Four-Node Shell Element
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## Definition
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A continuum-mechanics-based four-node shell element is a quadrilateral shell finite element whose behavior is derived from the three-dimensional continuum virtual work statement rather than from a specialized plate or shell theory.
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## How It Works
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The element represents shell geometry through a general four-node, non-flat quadrilateral description. It uses convected coordinates and a three-dimensional constitutive setting, while constraining the shell kinematics so the element can model thin and thick shells efficiently. The paper's central practical modification is a separate interpolation of transverse shear strains, which prevents the element from becoming overly stiff in thin-shell bending.
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The MITC4 implementation paper restates this lineage in an implementation-focused form: the four-node quadrilateral shell is treated as a three-dimensional continuum description degenerated to shell behavior, with all element degrees of freedom concentrated at the four vertices.
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[[On-the-Finite-Element-Analysis-of-Shell-Structures]] names the [[Basic Shell Mathematical Model]] as the underlying model for continuum-mechanics-based shell finite elements. That source makes the element's locking behavior a consequence of how well the discretization can approximate the model's bending, membrane, and transverse shear strain spaces.
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## Why It Matters
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Four-node shell elements are attractive in large structural models because they are computationally economical, but low-order shell elements can lock, distort poorly, or admit spurious modes. This formulation shows how a low-order element can remain useful for nonlinear shell analysis when the shear strain field and nonlinear kinematics are handled carefully.
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## Validation Thread
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The source tests the element against simple patch and rigid-body checks, classical shell benchmarks such as the Scordelis-Lo roof and pinched cylinder, large-deflection cantilever behavior, shallow spherical shell response, stiffened plate buckling, and elastoplastic circular plate response.
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The MITC4 source adds an [[OOFEM]] implementation thread, including patch tests and the [[Scordelis-Lo Shell Benchmark]] as the main convergence demonstration.
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## Connections
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- [[Assumed Transverse Shear Strain Interpolation]] is the locking remedy inside the element.
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- [[Total Lagrangian Shell Formulation]] is the nonlinear kinematic framework used for large displacement and rotation response.
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- [[Isoparametric Finite Elements]] supplies the mapping and integration context.
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- [[Nonlinear Finite Element Analysis]] supplies the incremental solution context.
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## Sources
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- [[A Continuum Mechanics Based Four-Node Shell]]
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- [[Four-Node-Quadrilateral-Shell-Element-MITC4]]
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- [[On-the-Finite-Element-Analysis-of-Shell-Structures]]
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