H.A. Mang:

"On Special Points on Load-Displacement Paths in the Prebuckling Domain of Thin Shells";

International Journal for Numerical Methods in Engineering,31(1991), 207 - 228.

Points on load-displacement paths of thin shells subjected to proportional loading, at which the second and/or third derivative of the displacement components with respect to the load parameter vanishes are termed 'special points'. Such points represent global characteristics of the state of deformation of the shell in the sense that for the respective valuesof the load parameter the metioned rate(s) of all displacement components at all points of the shell msut vanish. It will be shown that special points on load-displacement paths correspond to special points of one order lower on the Det K_T - \lamba diagram, where Det K_T is the determinant of the tangent stiffness matrix within the framework of the finite element method and \lambda is a dimensionless load parameter. Points of infelction on load-displacement diagrams, for example, correspond to extreme values on the Det K_T - \lambda diagram. The main reason for the occupation with special points on load-displacement paths is that points of inflection and flat points on these paths correspond to special points on eigenvalue curves in the context of accompanying linear stability analyses of geometrically nonlinear prebuckling analyses of thin shells by the fintite element method, investigated in a companion paper.

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