The state of stress at a point is completely determined when: 1. the stress vectors on three different planes are specified 2. the stress vectors on two different planes are speciale 3. the stress vectors one arbitrary plane is spec-
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
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
Unit #10- Principle of minimum potential energy and Castigliano's First Theorem Principle of minimum potential energy The principle of virtual displacements applies regardless of the constitutive law. Restrict attention to elastic materials(possibly nonlinear). Start from the Pvd
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