L3b_cae - 16.810 16.810 Engineering Design and Rapid Prototyping Engineering Design and Rapid Prototyping Instructor(s CAE-Finite Element Method

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Unformatted text preview: 16.810 16.810 Engineering Design and Rapid Prototyping Engineering Design and Rapid Prototyping Instructor(s) CAE -Finite Element Method January 16, 2007 Prof. Olivier de Weck Lecture 3b 16.810 (16.682) 2 Numerical Methods Finite Element Method Boundary Element Method Finite Difference Method Finite Volume Method Meshless Method 16.810 (16.682) 3 What is the FEM? Description- FEM cuts a structure into several elements (pieces of the structure).- Then reconnects elements at nodes as if nodes were pins or drops of glue that hold elements together.- This process results in a set of simultaneous algebraic equations. FEM: Method for numerical solution of field problems. Number of degrees-of-freedom (DOF) Continuum: Infinite FEM: Finite (This is the origin of the name, Finite Element Method) 16.810 (16.682) 4 Fundamental Concepts (1) Elastic problems Thermal problems Fluid flow Electrostatics etc. Many engineering phenomena can be expressed by governing equations and boundary conditions Governing Equation (Differential equation) ( ) L f + = Boundary Conditions ( ) B g + = 16.810 (16.682) 5 Elastic deformation Thermal behavior etc. Governing Equation: ( ) L f + = ( ) B g Boundary Conditions: + = [ ] { } { } = K u F A set of simultaneous algebraic equations FEM Approximate! Example: Vertical machining center Geometry is very complex! Fundamental Concepts (2) You know all the equations, but you cannot solve it by hand 16.810 (16.682) 6 [ ] { } { } = K u F 1 { } [ ] { } = u K F Property Behavior Action Elast Thermal Fluid Electrostat ic ic Behavior { } u Property [ ] K Action { } F stiffness displacement force conductivity temperature heat source viscosity velocity body for Dielectric permittivity electric potential ce charge Unknown Fundamental Concepts (3) 16.810 (16.682)16....
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This note was uploaded on 11/08/2011 for the course AERO 16.810 taught by Professor Olivierdeweck during the Winter '07 term at MIT.

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L3b_cae - 16.810 16.810 Engineering Design and Rapid Prototyping Engineering Design and Rapid Prototyping Instructor(s CAE-Finite Element Method

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