4/4/2008
Topic 4: Linear Constitutive Behavior
MEEM 5150
Spring 2008
First Law of Thermodynamics and
Strain Energy Density
First law of thermodynamics:
Under adiabatic conditions and static equilibrium:
The variation of work
body)
of the external forces (

4/3/2008
Topic 6-2: Beam Torsion
MEEM 5150
Spring 2008
Torsion of a Prismatic Bar of
Circular Cross Section
Twist angle
Deformation
Strain and stress
1
4/3/2008
Torsion of a Prismatic Bar of
Circular Cross Section
Boundary conditions
No normal force on th

2/5/2008
Topic 3: Strain
MEEM 5150
Spring 2008
One-dimensional strain measures
L
A
Take a 1D bar which can only be
streched axially. The bar had an
initial length L and area A that is
stretched to a final length of l and
area a. The engineering strain E
c

1/22/2008
Topic 1: Mathematical Preliminaries
MEEM 5150
Spring 2008
Scalar, Vector, Matrix and Tensor
Definitions
Scalar
Vector
Matrix
Tensor: Tensors may be classified by its rank or order N,
according to the transformation law they obey. This
classifica

Topic 5: Energy Methods
MEEM
MEEM 5150
Spring 2008
Principle of Stationary Potential
Energy
Virtual work:
Conservative system:
Castiglianos First Theorem
Example 5.1
Castiglianos Theorem on
Deflection
Based on the complementary energy C of the system
Line

1/24/2008
Topic 2: Stress
MEEM 5150
Spring 2008
Stress Notation
Stress components and body forces
1
1/24/2008
Properties of stress
Symmetry of components
Normal stress acting on an arbitrary plane
Shear Stress
Stress Transformation
Normal and Shear Stress

3/27/2008
Topic 6-1: Beam Bending
MEEM 5150
Spring 2008
Fundamental of Beam Bending
Centroidal Coordinate Axes (appendix B1-B3)
Moment of Inertia: Ix, Iy, J and Ixy
Parallel Axis Theorem
Principal Axes of Intertia
Plane of Load
Angle
Counter-clockwise fro

4/9/2008
Topic 7: Plate
MEEM 5150
Spring 2008
Introduction
Flat plate Middle surface lies in a plane
Thickness of a plate h is relatively small compared to middle
surface dimensions
Orthogonal curvilinear plate coordinates
Small deflection theory with con