김경종
46 lines
1.5 KiB
Markdown
46 lines
1.5 KiB
Markdown
---
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type: concept
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title: "Engineering Mathematical Models"
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complexity: intermediate
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domain: computational-mechanics
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aliases:
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- engineering model idealization
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- mathematical modeling
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created: 2026-05-28
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updated: 2026-05-28
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address: c-000007
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tags:
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- concept
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- modeling
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- finite-element-method
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status: current
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related:
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- "[[Finite Element Method]]"
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- "[[Computational Mechanics]]"
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sources:
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- "[[Finite Element Procedures]]"
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---
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# Engineering Mathematical Models
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## Definition
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Engineering mathematical models are idealized descriptions of physical systems, including geometry, material behavior, loads, boundary conditions, constraints, and the governing equations selected for analysis.
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## How It Works
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The analyst chooses a model that is simple enough to solve and rich enough to answer the engineering question. A finite element solution then approximates that selected model. If the model is poorly chosen, a numerically accurate result can still be physically misleading.
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## Why It Matters
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The source positions finite element analysis as part of an iterative engineering process: define the model, solve it, assess the result, compare against expected physical behavior, and refine the model when needed.
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## Connections
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- [[Finite Element Method]] solves mathematical models after discretization.
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- [[Mixed Finite Element Formulations]] and [[Nonlinear Finite Element Analysis]] are needed when the chosen model includes constraints, incompressibility, contact, or nonlinear material response.
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## Sources
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- [[Finite Element Procedures]]
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