add wiki

2026-05-28 17:16:48 +09:00
parent 665c5ab4e4
commit 4cc312954f
5693 changed files with 66683 additions and 4087 deletions
@@ -0,0 +1,59 @@
+---
+type: concept
+title: "Direct Time Integration Methods"
+complexity: advanced
+domain: computational-mechanics
+aliases:
+  - finite element dynamics
+  - direct integration
+  - Newmark method
+created: 2026-05-28
+updated: 2026-05-28
+address: c-000014
+tags:
+  - concept
+  - finite-element-method
+  - dynamics
+status: current
+related:
+  - "[[Finite Element Method]]"
+  - "[[Nonlinear Finite Element Analysis]]"
+  - "[[Nonlinear Newmark-Beta Integration]]"
+  - "[[Dynamic Buckling Analysis]]"
+  - "[[Finite Element Eigenproblem Solvers]]"
+sources:
+  - "[[Finite Element Procedures]]"
+  - "[[MITC Study Notes]]"
+  - "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
+---
+
+# Direct Time Integration Methods
+
+## Definition
+
+Direct time integration methods advance finite element equilibrium equations through time without necessarily transforming the problem into modal coordinates.
+
+## How It Works
+
+Dynamic finite element systems include mass, damping, stiffness, and time-dependent loading. The source covers central difference, Houbolt, Newmark, and Bathe methods, then analyzes approximation, load operators, stability, accuracy, numerical damping, and coupling of different integration operators.
+
+The MITC study notes add a focused nonlinear Newmark-beta derivation: Newton iteration is used at each time step, and Newmark relations express acceleration and velocity increments through the displacement increment.
+
+The dynamic buckling thesis uses time-dependent axial compression as the loading context. It connects dynamic response, natural frequency, and buckling instability boundaries rather than treating time integration as a standalone transient solve.
+
+## Why It Matters
+
+Time integration choices control stability, phase accuracy, numerical damping, and computational cost. Explicit methods can be efficient for very small stable time steps; implicit methods are more expensive per step but can support larger steps and nonlinear equilibrium iterations.
+
+## Connections
+
+- [[Finite Element Eigenproblem Solvers]] supports modal superposition and vibration analysis.
+- [[Nonlinear Finite Element Analysis]] couples time integration with nonlinear iteration.
+- [[Nonlinear Newmark-Beta Integration]] is the specific implicit nonlinear dynamics workflow extracted from the MITC notes.
+- [[Finite Element Heat Transfer and Field Problems]] uses related transient integration ideas for first-order field equations.
+
+## Sources
+
+- [[Finite Element Procedures]]
+- [[MITC Study Notes]]
+- [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]