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wiki/concepts/Direct Time Integration Methods.md

@@ -8,7 +8,7 @@ aliases:
   - direct integration
   - Newmark method
 created: 2026-05-28
-updated: 2026-05-29
+updated: 2026-06-02
 address: c-000014
 tags:
   - concept
@@ -26,6 +26,13 @@ related:
   - "[[Abaqus Eulerian and Particle Methods]]"
   - "[[Beam and Frame Finite Elements]]"
   - "[[Bar and Truss Finite Elements]]"
+  - "[[Elasto-Viscoplastic Finite Element Analysis]]"
+  - "[[Transient Dynamic Elasto-Plastic Analysis]]"
+  - "[[Midas FEA Linear Dynamics and Buckling Analyses]]"
+  - "[[Midas Civil Dynamic and Seismic Analysis]]"
+  - "[[Midas Civil Nonlinear Time History and Hysteresis Models]]"
+  - "[[Midas NFX Linear Dynamics and Buckling Analyses]]"
+  - "[[Midas NFX Nonlinear Static and Dynamic Algorithms]]"
 sources:
   - "[[Finite Element Procedures]]"
   - "[[MITC Study Notes]]"
@@ -33,6 +40,10 @@ sources:
   - "[[Abaqus Theory Manual]]"
   - "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
   - "[[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]]"
+  - "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
+  - "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
+  - "[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]"
+  - "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
 ---
 
 # Direct Time Integration Methods
@@ -55,6 +66,14 @@ The dynamic buckling thesis uses time-dependent axial compression as the loading
 
 [[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]] expands the production procedure choices: implicit direct integration, explicit dynamic analysis, direct-solution steady-state dynamics, modal dynamics, subspace steady-state dynamics, response spectrum, and random response analysis.
 
+[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]] adds the material-nonlinearity view of time integration: elasto-viscoplastic updates depend directly on time-step size, and transient dynamic elasto-plastic analysis couples inertia terms with evolving plastic zones.
+
+[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]] adds production time-history context: mode superposition and direct integration are treated alongside Rayleigh or modal damping, load-time interpolation, and practical time-step selection relative to modal periods and load intervals.
+
+[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]] adds civil seismic context: direct integration appears beside modal/Ritz analysis, damping choices, response spectrum procedures, multi-support excitation, nonlinear time history, and hysteretic member/link models.
+
+[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]] adds both linear and nonlinear transient details: HHT implicit integration, central-difference explicit integration, critical time-step control, artificial bulk viscosity, damping, mass scaling, residual-vector mode augmentation, and enforced-motion partitioning.
+
 ## 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.
@@ -69,6 +88,10 @@ Time integration choices control stability, phase accuracy, numerical damping, a
 - [[Abaqus Explicit Analysis Efficiency Techniques]] covers mass scaling, subcycling, and steady-state detection around explicit integration.
 - [[Abaqus Eulerian and Particle Methods]] uses explicit time integration for Eulerian, DEM, and SPH workflows.
 - [[Beam and Frame Finite Elements]] and [[Bar and Truss Finite Elements]] provide simple structural examples for mass-matrix construction.
+- [[Elasto-Viscoplastic Finite Element Analysis]] and [[Transient Dynamic Elasto-Plastic Analysis]] show how time stepping interacts with rate-dependent and plastic material state variables.
+- [[Midas FEA Linear Dynamics and Buckling Analyses]] connects time history analysis to Midas modal, response spectrum, and buckling procedure choices.
+- [[Midas Civil Dynamic and Seismic Analysis]] and [[Midas Civil Nonlinear Time History and Hysteresis Models]] connect time integration to seismic damping, multi-support excitation, and hysteretic bridge components.
+- [[Midas NFX Linear Dynamics and Buckling Analyses]] and [[Midas NFX Nonlinear Static and Dynamic Algorithms]] connect time integration to NFX modal superposition, explicit stability, HHT residual iteration, damping, and mass scaling.
 
 ## Sources
 
@@ -78,3 +101,7 @@ Time integration choices control stability, phase accuracy, numerical damping, a
 - [[Abaqus Theory Manual]]
 - [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]
 - [[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]]
+- [[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]
+- [[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]
+- [[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]
+- [[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]