modify wiki

2026-05-29 17:05:53 +09:00
parent b7f84e1c0f
commit b7b79e38b1
64 changed files with 3131 additions and 48 deletions
@@ -0,0 +1,56 @@
+---
+type: concept
+title: "Reduced Integration and Hourglass Control"
+complexity: advanced
+domain: computational-mechanics
+created: 2026-05-29
+updated: 2026-05-29
+address: c-000057
+aliases:
+  - reduced integration
+  - hourglass control
+  - under-integration
+tags:
+  - concept
+  - finite-element-method
+  - numerical-integration
+  - locking
+status: current
+related:
+  - "[[Abaqus Theory Manual]]"
+  - "[[Abaqus Element Library]]"
+  - "[[Isoparametric Finite Elements]]"
+  - "[[Solid Element Stiffness Integration]]"
+  - "[[Shell Locking Phenomenon]]"
+  - "[[Hybrid Incompressible Elements]]"
+sources:
+  - "[[Abaqus Theory Manual]]"
+---
+
+# Reduced Integration and Hourglass Control
+
+## Definition
+
+Reduced integration evaluates an element with fewer integration points than full quadrature. Hourglass control adds stabilization to suppress spurious zero-energy deformation modes that reduced integration can introduce.
+
+## How It Works
+
+Reduced integration can reduce computational cost and, in some element families, improve accuracy at special strain-sampling locations. It can also soften elements that otherwise become overly stiff in bending-dominated or nearly incompressible situations.
+
+The risk is rank deficiency: some displacement patterns can produce little or no strain energy at the reduced integration points. These patterns appear as hourglass or zero-energy modes. Abaqus controls them by adding artificial stiffness or related stabilization terms so the element remains usable without losing the intended benefits of reduced quadrature.
+
+## Why It Matters
+
+Reduced integration is not just a cheaper quadrature rule. It changes the numerical behavior of the element and must be judged together with element topology, mesh distortion, material behavior, contact, and expected deformation mode.
+
+## Connections
+
+- [[Isoparametric Finite Elements]] supplies the quadrature framework.
+- [[Abaqus Element Library]] places reduced integration among full, selective, and hybrid element choices.
+- [[Shell Locking Phenomenon]] is one reason under-integration or assumed-strain methods are introduced.
+- [[Hybrid Incompressible Elements]] is a more explicit mixed alternative for incompressible response.
+
+## Sources
+
+- [[Abaqus Theory Manual]]
+