16.21 Techniques of structural analysis and
design
Homework assignment # 3
Warmup exercises (not for grade)
Problem 3.23 from textbook
Problem 3.24 from textbook
Problem 3.25 from textbook
(Compliments of C. Gra.) Create a solid model of
the at plate

16.21 Techniques of Structural Analysis and
Design
Unit #9 Calculus of Variations
Let u be the actual conguration of a structure or mechanical system. u
satises the displacement boundary conditions: u = u on Su . Dene:
u = u + v, where:
: scalar
v : arbi

16.21 Techniques of structural analysis and design
Homework assignment # 4
Solidworks practice problem (Compliments of C. Gra. ) Create a solid model
for each of the following objects using Solidworks (you may turn in your le
electronically for feedback p

16.21 Techniques of structural analysis and
design
Homework assignment # 2
1. Determine whether the following stress elds are possible in a structural
member free of body forces:
(a) (not for grade)
11 = 3x1 + 6x2
12 = 4x1 + 3x2
22 = 5x1 + 4x2
(1)
(2)
(3)

16.21 Techniques of structural analysis and
design
Homework assignment # 1
Only problems 2, 3 and 4 are part of the assessment (contribute to the grade).
It is recommended that the assignment be done in Mathematica in its entirety
and turned in electronic

16.21 Techniques of Structural Analysis and
Design
Unit #1
In this course we are going to focus on energy and variational methods
for structural analysis. To understand the overall approach we start by con
trasting it with the alternative vector mechanics

16.21 Techniques of Structural Analysis and
Design
Unit #3 Kinematics of deformation
Figure 1: Kinematics of deformable bodies
Deformation described by deformation mapping :
x = (x) = x + u
1
(1)
We seek to characterize the local state of deformation of t

16.21 Techniques of Structural Analysis and
Design
Unit #2 Stress and Momentum balance
Stress at a point
We are going to consider the forces exerted on a material. These can be
external or internal. External forces come in two avors: body forces (given
pe

16.21 Techniques of Structural Analysis and
Design
Unit #2 Mathematical aside: Vectors,
indicial notation and summation convention
Indicial notation
In 16.21 well work in a an euclidean threedimensional space R3 .
Free index: A subscript index ()i wil

16.21 Techniques of Structural Analysis and
Design
Unit #5 Constitutive Equations
Constitutive Equations
For elastic materials:
ij = ij () =
U0
ij
(1)
If the relation is linear:
ij = Cijkl kl , Generalized Hookes Law
(2)
In this expression: Cijkl fourth

16.21 Techniques of Structural Analysis and
Design
Unit #4 Thermodynamics Principles
First Law of Thermodynamics
d
K +U =P +H
dt
(1)
where:
K: kinetic energy
U : internal energy
P : Power of external forces
H: hear exchange per unit time
1
K=
2
V
u u