POSITIVE DEFINITENESS AND COMPACTNESS OF TWO KINDS OF OPERATORS IN THEORIES OF ELASTIC STRUCTURES

【摘要】 <正> Relations exist between theories of elastic structures and the theory of elasticity in which the displacement field as well as the strain energy and kinetic energy expressions in the former is able to be derived from the latter by introducing appropriate simplified assumptions. Using such relations and some functional properties, this paper gives a unified proof of the positive definiteness of the ’structure theory operator’ and the compactness of the ’energy imbedding operator’ for various theories of elastic structures. Specifically, the conclusions are applicable to composite structures as well as to shells in general boundary conditions such as fixed edge, hinged edge, free edge, partially movable edge and their combinations. As significant consequences of the above conclusions, the existence of the weak solution of the equilibrium and vibration problems and the applicability of the Ritz method are assured for the theory of these elastic structures.更多还原

【Abstract】 Relations exist between theories of elastic structures and the theory of elasticity in which the displacement field as well as the strain energy and kinetic energy expressions in the former is able to be derived from the latter by introducing appropriate simplified assumptions. Using such relations and some functional properties, this paper gives a unified proof of the positive definiteness of the ’structure theory operator’ and the compactness of the ’energy imbedding operator’ for various theories of elastic structures. Specifically, the conclusions are applicable to composite structures as well as to shells in general boundary conditions such as fixed edge, hinged edge, free edge, partially movable edge and their combinations. As significant consequences of the above conclusions, the existence of the weak solution of the equilibrium and vibration problems and the applicability of the Ritz method are assured for the theory of these elastic structures.更多还原