Chapter 3
Stress I
Exercise 3.1 Check if the following Cartesian stress components are physically allowable:
2
3
ayz
dyz
dzy
bxz
dz(y x) 5
si j = 4 dyz
dzy
d(x y)z
cxy
and explain why (not). Here, cfw_x, y, z is short-hand for Cartesian coordinates cfw_

Chapter 7
Bending
Exercise 7.1 Consider a cantilever beam of length L := a + b that is subjected to a point force
F at a distance a from the clamp. Show that the tip deection is given by
w=
Fa2
(3L
6EI
a)
F
a
b
Hint: Split up the beam at x = a and use sup

Chapter 4
Stress II
Exercise 4.1 Consider a small rectangular plate, subject to a uniaxial stress state as illustrated
below.
A
11
11
45
e2
B
e1
(a) Cut this plate into two pieces along the line AB and use equilibrium to nd the normal
traction and the she

Chapter 2
Deformation
Exercise 2.1 Displacement is the difference between the current position of a material point
and its reference position, i.e. u = x X . In the case of a rigid body motion, u is uniform inside
the body. Consider the planar displacemen

Solution to Exer. 7.2
(a) The load P needed to deect the center of the beam by a displacement w in the y-direction
induces a bending moment M(x),
1 1
M = P( L x).
2 2
Substitution into the beam equation (3.49) and integration leads to the deection
W = w(x

Chapter 1
Maths
Exercise 1.1 Let a and b be two vectors with Cartesian components ai and bi , respectively.
(a) What are the Cartesian components of a b ?
(b) Write the corresponding matrix of components (for two-dimensional space).
Exercise 1.2 Simplify:

Solution to Exer. 3.3 This is a problem that is ideally suited to be solved by virtual work. For
this, we introduce two virtual strains that are work conjugate to the two stresses we are interested
in. The axial strain d ea is simply dened by considering

Solution to Exer. 2.1
(a) e is dimensionless
(b) Under the assumption that n > 0, the deformed shape looks like
W/2
H
(1)2H
(1+)W
representing extension in the x1 direction with contraction in x2 .
(c) The relative change in area is
(1
ne)(1 + e)2HW
2HW
2

INTRODUCTION TO
COMSOL Multiphysics
Introduction to COMSOL Multiphysics
19982015 COMSOL
Protected by U.S. Patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991;
8,457,932; and 8,954,302. Patents pending.
This Document

Solid Mechanics for Applied Physicists
Erik van der Giessen
2
Chapter 1
Mathematical preliminaries
1.1 Notation
I often try to tease mathematicians by saying that mathematics for me is just a language: whatever can be said in a mathematical way, could als

Chapter 2
The Mechanically Controlled Break
Junction ina)
Focus
Exercise 3.23 in the book is concerned with the Mechanically Controlled Break Junction
(MCBJ), which is a very elegant way to control the spacing between metallic electrodes with
subatomic re

Chapter 1
How to get started
1.1
Getting started
After ComSol has started, the initial screen will look something like this:
Then,
Click Model Wizard
Click 2D (planar)
Open Structural Mechanics, select Solid Mechanics (solid) and click Add
1
Once it h

Write name and student number on each page!
1
Homework
SOLID MECHANICS (NASM)
submission deadline: December 16, 2015 @11:59PM
Problem 1 For each of the following statements point out if it is correct or not, and why:
a. The elastic constants of a cubic cr

A few notes on scientic reporting
E. van der Giessen
Format of a scientic report
I. Introduction, including objectives (describe the technological setting that requires carrying out
the investigations reported)
II. Problem Formulation and Method of Analys

Write name and student number on each page!
Homework
SOLID MECHANICS (NASM)1
submission deadline: January 14, 2016 @11:59PM
This exam comprises four problems, for which one can obtain the following points:
Question
# points
1
2
3
4
1+1+1=3
1
1+1+2=4
2+1=3