For the potato-shaped body given in class to explain the concept of stress, the field of stress vectors t(n)=t(n)(x)on the plane of normal n given by its cartesian components(1,0, 0) known and its cartesian components are given by the expression

Concept Question Consider the following simple displacement field

16.21 Techniques of Structural Analysis and sig Spring 2003 Unit #4- Thermodynamics Principles First Law of Thermodynamics

Which of the following expressions represents the rate of work done by the stresses during the deformation of a body of an arbitrary material?

Strain energy and potential energy of a beam brec sedans hoMe the neutra xxis remain So Figure 1: Kinematic assumptions for a beam Kinematic assumptions for a beam: From the figure: AA'=u3(a1) Assume small deflections: B B\,BB\=3+ duy

Extend definition to material bodies: total work is the addition of the work done on all particles by forces distributed over the volume W by forces distributed over the surface t·udS

Constitutive Law(6 equations, O unknowns) C Bound dary conditions of two types Traction or natural boundary conditions: For tractions t imposed on the portion of the surface of the body aBt Displacement or essential boundary conditions: For displacement

Which of the following statements is correct? 1. The PVD only applies to linear elastic materials 2. The PVD applies only to elastic materials, but they can be linear or non-linear 3. The PVD applies regardless of the constitutive behavior of the material

Unit #9 -Calculus of Variations Let u be the actual configuration of a structure or mechanical system. u satisfies the displacement boundary conditions: u=u* on Su. Define

Concept Question Which of the following statements is true 1. The PVD and the PMPE are equivalent 2. The PVD is more general 3. The PMPE applies to any kind of material 4. The stationary character of the potential en ergy is equivalent to the Pvd for elastic ma terials