Which of the following expressions most ac curately and simply represents the comple mentary strain energy density Uc of a linear elastic material?

How can the paradox with the spring be plained? In other words, which of the following statements is true 1. Equilibrium can be derived from the equiv alence of the external and the internal work 2. Equilibrium is an artifact of our imagina- tion

which generalizes to the statement. This reduces the number of material constants from 81 to 54. In a similar fashion we can make use of the symmetry of the strain tensor This further reduces the number of material constants to 36. To further reduce the number of material constants consider the conclusion from the first law for elastic materials, equation

The following stress-strain curves were obtained for dif- ferent materials subjecting the specimen to the loading path(a, b, c, d ). Which one(s) of them correspond to elas- tic material(s)

For the uniform state of plane strain shown in the fig ure,which one(s) of the following statement(s) is(are valid?(Assume Poisson's ratio v+0)

We seek to characterize the local state of deformation of the material in a neighborhood of a point P. Consider two points P and Q in the undeformed

The following expression is the right statement of linear momentum balance for a deforming body of an arbitrary material

A Cauchy stress component at a given(fixed) point P of a structure in equilibrium under the action of external loads is defined when 1. the direction of the face on which the stress component acts is specified 2 the direction of the force from which the stress component is derived is specified None of the above statements

We are going to consider the forces exerted on a material. These can be external or internal. External forces come in two flavors: body forces(given per unit mass or volume) and surface forces(given per unit area). If we cut a body of material in equilibrium under a set of external forces along a plane as shown in fig. 1. and consider one side of it we draw two conclusions: 1 the equilibrium provided by the loads from the side taken out is provided by a set of forces that are distributed among the material particles adjacent to

16.21 Techniques of Structural Analysis and sig Spring 2003 Unit #1 In this course we are going to focus on energy and variational methods for structural analysis. To understand the overall approach we start by con- trasting it with the alternative vector mechanics approach