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?            A load cell intended to model forces applied to a specimen in a tensile testing machine            The seat-belt assembly in a vehicle            The solar panels on a communications satellite.            A compressor blade in a gas turbine engine            A MEMS optical switch            An artificial knee joint            A solder joint on a printed circuit board            An entire printed circuit board assembly            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