김경종
133 lines
6.3 KiB
Markdown
133 lines
6.3 KiB
Markdown
---
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type: concept
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title: "Finite Element Load Vector Assembly"
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complexity: intermediate
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domain: computational-mechanics
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created: 2026-05-29
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updated: 2026-06-02
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address: c-000068
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aliases:
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- equivalent nodal forces
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- finite element force vector
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- load vector assembly
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tags:
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- concept
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- finite-element-method
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- assembly
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- loading
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status: current
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related:
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- "[[Direct Stiffness Method]]"
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- "[[Finite Element Method]]"
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- "[[Beam and Frame Finite Elements]]"
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- "[[Plane Stress and Plane Strain Elements]]"
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- "[[Finite Element Thermal Stress Analysis]]"
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- "[[Abaqus Surface and Assembly Modeling]]"
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- "[[Abaqus Loads and Predefined Fields]]"
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- "[[Abaqus Prescribed Conditions and Amplitudes]]"
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- "[[Midas Civil Moving Load Bridge Analysis]]"
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- "[[Midas Civil Special Load and Design Utilities]]"
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sources:
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- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-I|Abaqus Analysis User's Guide Volume I]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-V|Abaqus Analysis User's Guide Volume V]]"
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- "[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]"
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source_refs:
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- source: "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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raw_path: ".raw/AFirstCourseInTheFiniteElementMethod/"
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raw_files:
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- "AFirstCourseInTheFiniteElementMethod_020.md"
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- "AFirstCourseInTheFiniteElementMethod_021.md"
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- "AFirstCourseInTheFiniteElementMethod_025.md"
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- "AFirstCourseInTheFiniteElementMethod_022.md"
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md_indices:
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- 20
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- 21
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- 25
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- 22
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Abaqus-Analysis-User-s-Guide-Volume-I|Abaqus Analysis User's Guide Volume I]]"
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raw_path: ".raw/AbaqusAnalysisUserGuide1/"
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raw_files:
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- "AbaqusAnalysisUserGuide1_068.md"
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- "AbaqusAnalysisUserGuide1_072.md"
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- "AbaqusAnalysisUserGuide1_064.md"
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md_indices:
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- 68
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- 72
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- 84
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- 64
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Abaqus-Analysis-User-s-Guide-Volume-V|Abaqus Analysis User's Guide Volume V]]"
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raw_path: ".raw/AbaqusAnalysisUserGuide5/"
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raw_files:
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- "AbaqusAnalysisUserGuide5_013.md"
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- "AbaqusAnalysisUserGuide5_012.md"
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- "AbaqusAnalysisUserGuide5_022.md"
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- "AbaqusAnalysisUserGuide5_018.md"
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md_indices:
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- 13
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- 12
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- 22
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- 18
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]"
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raw_path: ".raw/MidasCivilAnalysisReference/"
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raw_files:
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- "MidasCivilAnalysisReference_025.md"
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- "MidasCivilAnalysisReference_053.md"
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- "MidasCivilAnalysisReference_016.md"
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- "MidasCivilAnalysisReference_037.md"
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md_indices:
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- 25
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- 53
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- 16
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- 37
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match: "heuristic-heading-keyword"
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confidence: high
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---
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# Finite Element Load Vector Assembly
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## Definition
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Finite element load vector assembly converts applied loads into nodal force terms compatible with the element interpolation and then assembles those element force vectors into the global right-hand side.
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## How It Works
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Concentrated nodal loads can be placed directly into the global force vector. Distributed loads, body forces, surface tractions, heat sources, fluxes, and thermal strains must be converted into equivalent nodal terms before assembly.
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The source introduces this through distributed beam loading and later through body and surface forces in plane elements, equivalent nodal forces, and thermal force vectors. The same mapping principle is used: the load is weighted by the element interpolation or work-equivalent statement so that the nodal force vector performs the same virtual work as the original distributed load.
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The Abaqus user guide shows the production modeling counterpart: named surfaces are used to apply pressure, traction, radiation, pretension, coupling, and other surface-based model features before the solver converts them into finite element contributions.
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[[Abaqus-Analysis-User-s-Guide-Volume-V|Volume V]] broadens this to the full prescribed-condition layer: concentrated and distributed loads, thermal loads, electromagnetic loads, acoustic and shock loads, pore-fluid flow, pretension, connector loads and motions, and predefined fields all enter the model through procedure-compatible definitions and optional amplitudes.
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[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]] adds bridge load-generation workflows: moving vehicle positions, lane definitions, traffic surface lanes, support settlement combinations, wave forces, and unknown-load optimization all eventually need consistent conversion into structural load vectors or response envelopes.
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## Why It Matters
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Stiffness assembly alone does not define a finite element problem. Incorrectly transformed or assembled loads can produce wrong reactions, stress fields, and convergence behavior even when the element stiffness matrix is correct.
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## Connections
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- [[Direct Stiffness Method]] assembles load vectors alongside stiffness matrices.
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- [[Beam and Frame Finite Elements]] use equivalent nodal forces for distributed loads.
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- [[Plane Stress and Plane Strain Elements]] require body and surface force vectors.
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- [[Finite Element Thermal Stress Analysis]] treats thermal strain as an equivalent initial force contribution.
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- [[Abaqus Surface and Assembly Modeling]] supplies the named surfaces used by production input files for many distributed loads.
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- [[Abaqus Loads and Predefined Fields]] catalogs the Abaqus load and field workflows.
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- [[Abaqus Prescribed Conditions and Amplitudes]] controls how loads vary through step or total time.
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- [[Midas Civil Moving Load Bridge Analysis]] and [[Midas Civil Special Load and Design Utilities]] connect load assembly to vehicle placement, settlement, wave, and optimization-generated load cases.
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## Sources
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- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]
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- [[Abaqus-Analysis-User-s-Guide-Volume-I|Abaqus Analysis User's Guide Volume I]]
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- [[Abaqus-Analysis-User-s-Guide-Volume-V|Abaqus Analysis User's Guide Volume V]]
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- [[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]
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