THE EQUILIBRIUM OF AN ISOTROPIC ELASTIC PLATE. 
TABLE 
’ IyrRopucToRY ANALYSIS 
(a) to (g). Evaluation of definite neon sewing 
the Bessel functions. Degenerate cases 
(h). Potential functions derived by integration from 
the point- -source potential. Definite integral 
expressions for these . : 
(0), (j). Solution of the problem of flow hei 
two infinite parallel aaa Main stream 
and local currents 
(k). Curvature. Differentiation as to arc siti 
normal 
§ 1. Equations of equilibrium. Form of solution 
for a plate free from bodily force 
Force applied at a single point of an eae 
solid . 
Solution of the preclern of Oneal aabon 
for an infinite plate . 
Flexural and extensional poiaponeats of the 
strain. Disadvantages of the solution in 
definite integrals 
§ 5. Transformation of the definite integrals into 
” series, by means of Cauchy’s Theorem of 
contour integration é : 
Types of the particular solutions. agrees 
the general solution 
Position of the zeroes of the Henge oan 
CEC - 
§ 8. Approximate fens) of the nth fers of the 
infinite series, when n is large 
§9. The solution for arbitrary normal traction. 
Questions for discussion 
§ 10. Detailed solution of a special case. 
term differentiations . 
§ 2. 
§ 3, 
§ 4. 
§6. 
Si 7. 
Merit = 
Siemation of 
§11. The same special problem. 
two infinite series ‘ 
§ 12. Final form of the same special clean 
$13. Order of magnitude of the various parts of 
the solution when the thickness of the 
plate is small . - : 
§ 14. Methods and results of the peal case eXx- 
tended to the general problem of arbitrary 
normal traction . 
§ 15. Independent symbolical golution a the 
general problem . 
§16. The problem of tangential face fraction! 
Solution for an element of traction. 
§ 17. Composition of the solution . 5 : 
§ 18. General solution. Comparison with the 
solution for normal traction 
§ 19. Normal force applied at a single internal 
point. Solution in definite integrals 
§ 20. The same solution in series 
OF 
PAGE 
132 
132 
135 
136 
139 
140 
142 
143 
145 
147 
154 
155 
156 
CON TEN Ts. 
131 
PAGE 
§ 21. Solution of a special problem of internal 
areal normal force 170 
§ 22. Approximate forms of displacements and 
stresses in the general case . 173 
§ 23. Normal force of constant intensity Simowsinows 
the thickness : 175 
§ 24. Internal force parallel to the be 176 
§ 25. Solution 2 : é c 178 
§ 26. Approximate neat! Lagrange’s equation 
for flexure to a second approximation 180 
§ 27. Extensional strain. Differential wees of 
the principal mode 5 lisiil 
§ 28. Approximate values of the sine across a 
plane parallel to the faces . 82 
§ 29. Transmission of force to a distance. Expan 
sions in polar coordinates . 183 
§ 30. Types of deformation conveying a chen 
resultant stress . 185 
§ 31. Conditions for the existence of a ingen with 
finite potential energy. Elastic equivalence 
of statically equipollent loads 187 
§ 32. Bétti’s reciprocal theorem. Verification of 
preceding solutions c > LBS 
§ 33. Finite plate under edge secon, Form of 
the solution Bedeeed by means of Betti’s 
Theorem 192 
§ 34, The same by another seal : 195 
§ 35. General solution for an infinite solid under 
any forces . : 196 
§ 36. Bettis Theorem and the sahil of ica 
edge tractions é 197 
§ 37. Exact solutions of special problems for a 
circular plate. Problem aan 
transverse displacement 198 
§ 38. Problem 2 — normal displacement and nor- 
mal shearing stress given. The Fourier 
and other ‘methods of obtaining such 
solutions 201 
$39. Problem 3 — permanent modes ane io sym- 
metrical edge tractions - 205 
§ 40. Expansions of arbitrary functions . 206 
§ 41. The problem of given edge tractions for a 
thin plate . 208 
§ 42. Extensioral strain 208 
§ 48. The Green’s function method for the per- 
manent mode 213 
§§ 44, 45. Flexural strain. Solutions to first and 
second approximation 218, 220 
§ 46, Flexural strain. The Green’s function 
method. Kirchhoff’s boundary conditions 
to a second approximation 224 
228 
Addition to Paper 
