Page:Love, A.E.H. - A treatise on the mathematical theory of elasticity (1920).djvu/17



144. 145. 146. 147. 148. 149. 150. 151. . 153. 154. 155. . PAGE

Introductory. ... ..... 202 Displacement corresponding with plane strain 202 Displacement corresponding with plane stress ... . 204 Generalized plane stress 206 Introduction of nuclei of strain 206 Force operative at a point 207 Force operative at a point of a boundary 208 Case of a straight boundary 209 Additional results : (i) the stress function, (ii) normal tension on a segment of a straight edge, (iii) force at an angle, (iv) pressure on faces of wedge 209 Typical nuclei of strain in two dimensions 211 Transformation of plane strain 213 Inversion 213 Equilibrium of a circular disk under forces in its plane, (i) Two opposed forces at points on the rim. (ii) Any forces applied to the rim. (iii) Heavy disk resting on horizontal plane. . 215 Examples of transformation 217 

Appendix to Chapters VIII and IX. Volterea's Theory of Dislocations a. Introductory, (a) Displacement answering to given strain. (6) Discon- tinuity at a barrier, (c) Hollow cylinder deformed by removal of a slice of uniform thickness, {d) Hollow cylinder with radial fissure



Chapter X. Theory of the integration op the equations of equilibrium of an isotropic elastic solid body . Nature of the problem . R&ume of the theory of Potential. . Description of Betti's method of integration. . Formula for the dilatation .... . Calculation of the dilatation from surface data . Formulse for the components of rotation. . Calculation of the rotation from surface data. . Body bounded by plane — Formulae for the dilatation . Body bounded by plane — Given surface displacements . Body bounded by plane — Given surface tractions . Historical Note . Body bounded by plane — Additional results. . Formulse for the displacement and strain . Outlines of various methods of integration 228 230 231 233 234 235 235 237 239 241 242 243 245