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wiki/concepts/Scordelis-Lo Shell Benchmark.md

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+---
+type: concept
+title: "Scordelis-Lo Shell Benchmark"
+complexity: intermediate
+domain: computational-mechanics
+aliases:
+  - Scordelis-Lo shell
+  - cylindrical Scordelis-Lo shell
+  - Scordelis Lo roof
+created: 2026-05-28
+updated: 2026-05-28
+address: c-000024
+tags:
+  - concept
+  - finite-element-method
+  - shell-elements
+  - benchmark
+status: current
+related:
+  - "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
+  - "[[Shell Structure Asymptotic Behavior]]"
+  - "[[Shell Element Benchmark Testing]]"
+  - "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
+  - "[[MITC4 Shell Element]]"
+  - "[[Continuum Mechanics Based Four-Node Shell Element]]"
+  - "[[Static Equilibrium Equation Solvers]]"
+sources:
+  - "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
+  - "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
+---
+
+# Scordelis-Lo Shell Benchmark
+
+## Definition
+
+The Scordelis-Lo shell benchmark is a classical cylindrical shell problem used to evaluate shell finite elements under bending and membrane action.
+
+## How It Is Used
+
+In the MITC4 source, the shell is loaded by dead weight and symmetry allows one quarter of the structure to be modeled. The response quantity is the displacement at point B, and mesh refinement is used to compare MITC4 convergence with an RDKT reference element and an analytical reference.
+
+[[On-the-Finite-Element-Analysis-of-Shell-Structures]] uses the Scordelis-Lo roof shell as an asymptotic-behavior example. The paper identifies it as a mixed-dominated shell benchmark with an approximate load scaling factor of `rho = 1.75`, which makes it useful for exposing locking and non-uniform convergence.
+
+## Why It Matters
+
+The benchmark is useful because shell elements must couple membrane and bending behavior without becoming artificially stiff. Poor shell formulations can pass simple tests yet converge slowly or incorrectly on this curved-shell problem.
+
+## Reported Trend
+
+The source reports MITC4 displacement magnitudes converging from about 3.43 on a `4x4` quadrilateral mesh to about 3.61 on `32x32` and `64x64` meshes. The RDKT comparison converges to about 3.60 on the same refinement sequence.
+
+## Connections
+
+- [[MITC4 Shell Element]] uses this benchmark as its primary performance demonstration.
+- [[Continuum Mechanics Based Four-Node Shell Element]] includes the benchmark family in the broader Dvorkin-Bathe shell validation thread.
+
+## Sources
+
+- [[Four-Node-Quadrilateral-Shell-Element-MITC4]]
+- [[On-the-Finite-Element-Analysis-of-Shell-Structures]]