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강의내용
1. 유한요소법이란 ?
2. 스프링요소방정식의유도
3. 트러스와프레임요소방정식의유도
4. 평면요소방정식의유도
5. 변분법을이용한유한요소정식화
6. 가중잔차법을이용한유한요소정식화
7. 형상함수와보간
8. 등매개변수요소의정의
9. 수렴조건10.요소방정식의적분
11.부록SIT 2004 2
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• 본강의노트의내용은㈜베이시스에서제공한 VISUALFEA 멀티미디어를이용한유한요소법강의자료에서발췌사용하였읍니다.
참고 ( http://www.visualfea.com/ )
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1. 유한요소법이란 ?
편미분방정식
예를들면딱딱하고매끈한탁자위
•근사해 -> 유한요소법은항상틀린답을준다. 오차의정도가중요.•정답을모르면, 유한요소해석을믿어서는안된다. 검증이중요.
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간단한예: 원의근사
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예를들면, 각요소안에변형률이나응력을구해진변위를이용하여계산한다.
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2. 스프링요소방정식의유도
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Discrete Member
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강성계수: 단위변위를일으키는데필요한힘
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2자유도
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3자유도스프링요소의강성도의계산
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또는두스프링의강성계수의합으로표시될수있다.
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자유도
절점번호
요소번호
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3.트러스/프레임요소방정식의유도
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트러스는삐딱하게사용될수있다.
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절점력정의 절점변위정의Discrete member
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자유도방향으로분력의방향을맞추면..
자유도방향으로분력을계산하면,
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Discrete member
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유한요소방정식의정식화
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4. 평면요소방정식의유도
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절점변위와절점력의관계식을구하는것이목표
절점변위-변위(분포)관계
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요소의길이
요소의변위
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구조물안의임의의한점에서의변위
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?절점변위와변형률의관계를구하려면,
?
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절점변위와요소내임의점의변위의관계식을먼저구해야한다.
?
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요소의거동을시행해 (형상함수) 로가정한다.
형상함수
a0 ~ a5: 미정계수
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G의역행렬
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절점력과응력의관계를구하자.
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절점력과응력의관계를구한다.
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절점력과절점변위의관계는다음과같다.
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절점력과절점변위관계요약
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5. 변분법을이용한유한요소정식화
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6. 가중잔차법을이용한유한요소정식화
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7. 형상함수와보간
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1차요소
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2차요소
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n차요소
LAGRANGE POLYNOMIAL
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이동자유도만 이동/회전 자유도 갖음
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8. 등매개변수요소의정의
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9. 수렴조건: 요소를작게만들때해에수렴하는조건
•연속성의조건•완전성의조건
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균일경사상태조사방법
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10. 요소방정식의적분
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11. 전처리와후처리
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Classification of Solid-Mechanics ProblemsAnalysis of solids
Static Dynamics
Behavior of Solids
Linear Nonlinear
Material
Fracture
GeometricLarge Displacement
Instability
Plasticity
ViscoplasticityGeometric
Classification of solids
Skeletal Systems1D Elements
Plates and Shells2D Elements
Solid Blocks3D Elements
TrussesCablesPipes
Plane StressPlane StrainAxisymmetricPlate BendingShells with flat elementsShells with curved elements
Brick ElementsTetrahedral ElementsGeneral Elements
Elementary Advanced
Stress Stiffening
부록
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Information Available from Various Types of FEM Analysis
• Static analysis» Deflection » Stresses » Strains » Forces » Energies
• Dynamic analysis» Frequencies » Deflection (mode
shape) » Stresses » Strains » Forces » Energies
• Heat transfer analysis»Temperature » Heat fluxes » Thermal gradients » Heat flow from convection faces
• Fluid analysis» Pressures » Gas temperatures » Convection coefficients » Velocities
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Example FEM Application Areas
• Automotive industry» Static analyses » Modal analyses» Transient dynamics » Heat transfer » Mechanisms » Fracture mechanics » Metal forming » Crashworthiness
• Aerospace industry» Static analyses » Modal analyses» Aerodynamics » Transient dynamics » Heat transfer » Fracture mechanics » Creep and plasticity analyses » Composite materials » Aeroelasticity » Metal forming » Crashworthiness
• Architectural» Soil mechanics» Rock mechanics» Hydraulics» Fracture mechanics» Hydroelasticity
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Commercially Available FEM Software Suites (partial list)
Software Package Introduced CommentsABAQUS 1978 General purpose, with special emphasis on advanced linear and nonlinear structures and heat transfer applications.ADINA 7.0 1975 Optimized for structural and heat transfer applications. Limited element library. Extensive material model library.
ALGOR 1984 First FEM package available for PC use. ANSYS/LS-DYNA N/A For solving highly nonlinear structural dynamics problems (impact, large deformation, nonlinear materials, etc.)
ANSYS/MECHANICAL 1970 Probably the best-known and most widely-used FEM software. Complete structures/thermal/acoustics modleing.ANSYS/Multiphysics N/A Coupled-field, multidisciplinary FEM program.
ELFEN N/A Includes linear and nonlinear buckling, modal analysis, transient heat transfer analysis, impact and fragmentation.GENESIS N/A Fully integrated finite element analysis and numerical optimization software for structural analysis.
LUSAS N/A Includes automatic meshing, advanced non-linear analysis, and composites analysis.MARC 6.2 1970 3D automated contact analysis capabilities suited for studying tough manufacturing problems, (metal forming/ etc.)MSC/FEA 1971 MSC participated in the 1965 development of NASA's public-domain FEM code, NASTRAN.
MSC/NASTRAN for Windows N/A Handles stress, vibration, dynamic, nonlinear, heat transfer, and fluid flow analyses of mechanical components.NISA/DISPLAY 1973 A family of general purpose FEM programs for PCs and workstations. Modular design.
PAM 1973 FEM software optimized to study restraint systems (PAM-SAFE), impacts (PAM-SHOCK) and metal forming.SAMCEF 1965 One of the oldest FEM codes available. A powerful FEM package for structural and heat transfer analysis.
STARDYNE 1967 The world's first commercially available Finite Element Analysis software.STARS N/A Integrated, general-purpose, finite element software. Developed by NASA.
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Selected FEM Resources on the Internet
http://www.comco.com/feaworld/feaworld.html-Extensive FEM links, categorized by analysis type (mechanical, fluids, electromagnetic, etc.)
http://www.engr.usask.ca/%7Emacphed/finite/fe_resources/fe_resources.html- Lists many public domain and shareware programs.
http://sog1.me.qub.ac.uk- Home page of the the Finite Element Research Group at The Queen's University of Belfast. Excellent set of FEM links.
http://www.tenlinks.com/cae/-Hundreds of links to useful and interesting CAE cited, including FEM, CAE, free software, and career information.
http://www.nafems.org/- National Agency for Finite Element Methods and Standards (NAFEMS).
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http://www.dermotmonaghan.com/- provides an overview and history of FEA/FEM, information on mesh
generation and various analysis types, advice on buying FEA software and services, plus related links and resources, by Dermot Monaghan
http://www.6dof.com/new - independent resource, functions mainly as a forum but also has links,
articles, more
http://www.tsdengineering.com/- FEA techniques on convergence, meshing, assemblies, vibration and heat
transfer, developed for Pro/MECHANICA but useful in a general
http://www.tak2000.com/- this resource for thermal designers and analysts provides free thermal
data, FAQs and many links to thermal consultants, agencies and products and companies. From K&K Associates, who also makes TAK 2000, a general-purpose thermal analyzer.
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References (참고도서)
Cashman, J., 2000. “Future of Engineering Simulation,” ANSYS Solutions, Vol. 2, No. 1, pp. 3-4.
Chandrupatla, T. R. and Ashok D. Belegundu, 1997. Introduction to Finite Elements in Engineering, Prentice Hall, Upper Saddle River, New Jersey.
Kardestuncer, H., 1987. Finite Element Handbook, McGraw-Hill, New York.
Krouse, J., 2000. “Physical Testing Gets a Bum Rap,” ANSYS Solutions, Vol. 2, No. 2, p. 2.
Lentz, J., 1994. Finite Element Analysis Cross Training, unpublished lecture notes, Honeywell Engines and Systems, Phoenix, Az.
Nikishkov, G.V., 1998. Introduction to the Finite Element Method, unpublished lecture notes, University of Arizona, Tucson, Az.
Rajan, S.D., 1998. Finite Elements for Engineers, unpublished lecture notes, Arizona State University, Tempe, Az.
Segerlind, L. J., 1984. Applied Finite Element Analysis, John Wiley and Sons, New York.
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유한요소법공개강좌계획
Weekly based open lecture: • 매트릭스구조해석 + 유한요소법이론과프로그래밍• 기본수치해석이론, 판이론, 쉘이론, 비선형해석, 동적해석
• Mesh Generation• Postprocessing using Computer Graphics and
Virtual Reality Technology• Software Package Development using GUI.• Clustering of Linux machines for Parallel Processing
예정일자: 미정
