FORMULATION OF 2 AND 3 DIMENSIONAL BVPs
Laplacian Equations, e.g. Heat Conduction, Incompressible Potential Flow
NSD # of space dimensions
open set, domain (not including boundary)
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First rule of Ugly Method: don't use Ugly Method. It is much easier and quicker and more reliable to use the "grouping" method to construct bond
Common effort / common flow
A system consisting of two elements shares both an effort, and a flow. (Shares magnitude, but not necessarily sign)
A system consisting of three elements is either common effort (0-junction) or common fl
1. Sketch, reduce and annotate bond graph models of the following systems. Gravity
acts downward in all cases and there is no friction.
2. Sketch, reduce and annotate a bond graph model of the following system. There is
friction between m1 and ground. Con
1. Consider the circuit below.
Develop a bond graph for the circuit. Reduce and annotate.
Identify state variables.
Write junction relations and constitutive relations in proper causal form.
Find state equations.
2. The purpose
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You can (and should) reduce a bond graph as far as possible using the reduction rules below. This makes your subsequent work easi
ME 390 INTRODUCTION TO DYNAMIC SYSTEMS
1. Write a differential equation for x(t) using this block diagram:
You can assume that u(t) is a known input function.
2. Consider a tower crane of the
Dynamic variables and modeling
When you make a physical diagram (picture, circuit diagram,
etc) be sure to show each element distinct from all the others.
This can be easily overlooked for an effect like gravity (you
tend to think of it as part of the mas
Arbitrary Causality and State Equation Loops
When assigning causality to your bond graph, if you find that you can arbitrarily assign
the causality of your resistive elements, you will hit a loop when deriving your state
MANE 4240 & CIVL 4240
Introduction to Finite Elements
Prof. Suvranu De
Higher order elements
Properties of shape functions
Higher order elements in 1D
Higher order triangular elements (using area coordinates)
Section 4: Implementation of Finite Element
Analysis Other Elements
1. Quadrilateral Elements
2. Higher Order Triangular Elements
3. Isoparametric Elements
Implementation of FEA:
Section 4.1: Quadrilateral Elements
Refers in general
[Ref: Jacob Fish and Ted Belytschko, The first Course in Finite Element, John Wiley & Son, 2007]
1. FOURIER LAW (LIKE HOOKES LAW FOR STRESS ANAYSIS)
HEAT FLUX =
2. CONSERVATION OF ENEGY
3. T C
1D Elasticity (Boundary Value Problem (BVP) or Strong Form)
Given a bar of cross-sectional area A(x), with thermal expansion coefficient (x), temperature
distribution t(x), Youngs modulus E, acted on by a body force per unit volume b(x), find: u(x)
ME-CEE 327 Finite Element Methods in Mechanics Fall 2016
Professor Wing Kam Liu with Dr. Mark Fleming of Caulfield Engineering as Guest Lecturer
Days and Times:
Tu, Th 12:30pm-1:50pm, Tech LR2
Professor Wing Kam Liu: Tu Th 11:15a
% CEE-ME_327 computer homework #1 %
%= Preprocessing =%
nel=5; % number of elements
totlength=10; % total length of the domain
b = 10; % body force [force/length]
youngs=1; % elastic modulus
area=1; % element area
nne=2; % number of nodes in an ele
Computer Homework #1
Starting with the attached Matlab code, develop a program for onedimensional elasticity. The parts that need to be added are the
computational of strain and stress. The program should be able to treat
an arbitrary numb
Tension and Compression in Bars
1 Tension and Compression in
Constitutive Law .
Single Bar under Tension or Compression.
Statically Determinate Systems of Bars .
Statically Indeterminate Sys
About Bond graphs - The System Modeling World
Page 1 of 25
About Bond Graphs
2. Power variables
3. Standard elements
4. Power directions
5. Bond numbers
7. System equations
9. Example models
10. Art of creating m