The Optimization Of Thermal Plate And Shell Structures

The engineering structures that work at high temperatures are called thermal structures.When temperature changes,deformation occurs in the plate and shell structures,which are common in the industrial equipment.If the structure is constrained by the boundary,moments and stresses are generated inside it.How to minimize thermal deformation and thermal stress has always been a hot topic for scholars.This thesis starts with the discussion of strain energy,derives the optimal criterion for plate and shell under non-uniform temperature field.Strain energy under thermal load differs from that in traditional problem.Strain energy is produced by the combination of mechanical strain and stress.In this thesis,a method of constructing a virtual displacement field is proposed to simplify the derivation process.The iteration format in non-uniform temperature field is derived.The first part of this thesis studies the optimization of plate structure and proposed an optimization criterion by the variation principle.This optimization criterion can be used to deal with the optimization of plate under non-uniform temperature field with volume constrain.Then we provide several numerical examples.In the second part of this thesis,we study the iterative format of the shell thickness optimization in the form of new strain energy.By constructing the virtual displacement field,the paper derives the optimal iteration format for the thickness optimization under non-uniform temperature field.The optimality criterion is compared with other two heuristic criteria which each only contains sectional moments or membrane forces.Several numerical examples show that similarity and effectiveness of optimization results are dependent on the structural shape.The third part of this thesis studies the optimal iteration format for shell with a more general shape.A number of examples are given,which show that the criterion can reduce the thermal deformation.Finally,the paper summarizes the optimal criteria and discusses possible direction in the future research.