GENERAL SOLUTIONS FOR THREE-DIMENSIONAL THERMO-ELASTIC PROBLEMS OF TWO-DIMENSIONAL QUASICRYSTALS

摘要

The three-dimensional thermo-elastic problems of two-dimensional hexagonal quasicrystals are systematically investigated.Four displacement functions F,f,G and g are introduced to represent the displacement components in the equilibrium equations.Then the three-dimensional thermo-elastic problems are decoupled into two uncorrelated problems:the problem I associated with displacement functions F,G,u3 and temperature T,and the problem II associated with displacement functions f and g.Two higher-order displacement functionsHandHare introduced,which are eighth-order and fourth-order,respectively for problem I and problem II.For further simplification,a decomposition and superposition procedure is taken to replace the two higher-order displacement functions with six quasi-harmonic displacement functions,respectively.The general solutions obtained for problem I and II are in simple forms which are all applied conveniently.