Problems for Chapter 1
Objectives and Methods of Solid Mechanics
1.1. Defining a problem in solid mechanics
1.1.1. For each of the following applications, outline briefly:
- What would you calculate if you were asked to model the component for a design application?
- What level of detail is required in modeling the geometry of the solid?
- How would you model loading applied to the solid?
- Would you conduct a static or dynamic analysis? Is it necessary to account for thermal stresses? Is it necessary to account for temperature variation as a function of time?
- What constitutive law would you use to model the material behavior?
126.96.36.199. A load cell intended to model forces applied to a specimen in a tensile testing machine
188.8.131.52. The seat-belt assembly in a vehicle
184.108.40.206. The solar panels on a communications satellite.
220.127.116.11. A compressor blade in a gas turbine engine
18.104.22.168. A MEMS optical switch
22.214.171.124. An artificial knee joint
126.96.36.199. A solder joint on a printed circuit board
188.8.131.52. An entire printed circuit board assembly
184.108.40.206. The metal interconnects inside a microelectronic circuit
1.1.2. What is the difference between a linear elastic stress-strain law and a hyperelastic stress-strain law? Give examples of representative applications for both material models.
1.1.3. What is the difference between a rate-dependent (viscoplastic) and rate independent plastic constitutive law? Give examples of representative applications for both material models.
1.1.4. Choose a recent publication describing an application of theoretical or computational solid mechanics from one of the following journals: Journal of the Mechanics and Physics of Solids; International Journal of Solids and Structures; Modeling and Simulation in Materials Science and Engineering; European Journal of Mechanics A; Computer methods in Applied Mechanics and Engineering. Write a short summary of the paper stating: (i) the goal of the paper; (ii) the problem that was solved, including idealizations and assumptions involved in the analysis; (iii) the method of analysis; and (iv) the main results; and (v) the conclusions of the study