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Differentiation and integration are performed, rendering a function. 4. The resulting function is minimized using differential calculus. itz Method for Steering Link Using the Ritz method, the variational calculus problem of minimizing a functional is replaced by the less complicated, approximate, ~z~erentiaZ calculus problem of minimizing a function. 17. ".. 1) can be established by examining the strain energy in a differential size slice of a rod-like structure, or by manipulating the governing differential equation; both techniques are briefly mentioned in Appendix B.

The equations for strain given above are applicable for "small" strains and displacements. 8). 8) are sometimes called Green-Lagrangestrain; Cook [11, p. 47). " Ford [lo,p. 1211, suggests that normal strains less than 1 percent can be considered small, while Bathe [12, p. 3031 suggests normal strains less than 4 percent can be considered small. 001 radian are small according to Malvern [13, p. 12l]. The small strain assumption is valid for many well designed structures that are constructed of typical engineering metals.

The constant term, fo, is added to account for the possibility of a non-homogeneous boundary condition. The Ritz method can also be utilized for solid mechanics problems in two- and threedimensional space. In the three-dimensional case, each trial function could be a function of three spatial coordinates, x, y, and z, for instance. art it ion in^ a Structure The finite element method, when used to solve solid mechanics problems, is essentially the same as the Ritz method illustrated above. The finite element method establishes a functional, specifies displacement assumptions, and performs a mini~zationprocess.