Study On Element Technique Of The RC Structures And The Optimal Design Of Discrete Variables

This thesis lays a theoretical foundation to the project Study on Automatic Process ofOptimal Design for Reinforced Concrete Structures of Henan Foundation of NaturalScience(Code: 99110114). Its main purpose is on systematical research of reinforcedconcrete (RC) discrete element and its optimality calculation method. In general, the elements to simulate the reinforced concrete structures can be dividedinto 3 kinds, that is separate model, homogeneous model and combined model. In theseparate model, the tendon and concrete are meshed as different materials respectively byrod elements and triangle or quadrangle plane elements (for plane problems). It is able toreflect the real constitution of the RC members, as well as to simulate the conjunction andslippage between the tendon and concrete. On the other hand, more elements are neededso that the amount of computation work increases greatly, since the diameter of tendons isusually much smaller than the dimensions of concrete. In the homogeneous model, thefunction of tendons is assumed to be uniform in some approximated way in order to forman equivalent homogeneous material within concrete. The formulation of thehomogeneous model is same with that of general FEM for common continuum, let alonethe elastic matrix being resultant of that of tendon and concrete. The computation issimple, but the approximate assumption makes this method cannot be generalized, becauseit only represents the constitution and function of tendons in such a rough way, that thenumerical results are inaccurate. In the combined model, the function of tendon(s) isconsidered by the stiffness matrix with rod element, then add it into the stiffness matrix ofconcrete by a rational way. So that it can express the function of tendon(s) and constitutionof RC member, without increasing of degree of freedom. Investigating deeply about both of the combined and homogeneous elements for RCstructures shows that the actual function of tendon is commonly under-estimated, so thatthe design based on these theories may led to wasting of steel. Therefore, the author takesaccount the constructive features of the Reinforced Concrete structures to raise theconcepts of identical and un-identical displacement field, and to establish new elementsfor plane and space RC structures, including plane quadrangle element with severaltendons, plane triangle element with one tendon or several tendons, block element with Vseveral tendons and so on. According to the formulae of the stiffness matrices and theprinciple of hardening, the author proposes new plane triangle and quadrangle elements,block element, beam element and shell element for RC structures under the un-identicaldisplacement field, which are more rational to describe the mechanical performance forthe RC material as well as the actual function of tendons in RC structures, derivesformulae of stiffness matrices of these elements in the identical and un-identicaldisplacement field respectively. In light of the features of discrete variable, the author presents concept of the virtual3-D space and proves the relevant theorems. The author also puts forward ideas of directmesh, virtual direct mesh, virtual-real mesh and equivalent mesh as well as thecorresponding design space to make the optimal method more specific. The design spaceD# of discrete variables is set up by mesh design space, probable values of the discrete (n)variable and the features of RC structures. 3 kinds of optimality calculation methods fordiscrete variables are proposed on the basis of design space, i.e. virtual-real mesh method,complex shape method and the topological sorting method. These research work provide ageneral thinking model for exploring the optimization design method of discrete variables,that is: establishing the mesh node set Dn (M ) of value-assignable discrete variables,decreasing the range of the value assignable by combining that the feature...