Modes Identification And Concept Design Of Plane Structures Based On Deformation Decomposition

Engineering structure design consists of three stages: concept design,calculation design and constitution design. Generally known, problems about the strength,absolute stiffness and stability of structures and components are the main studying contents at the calculation and constitution design stages. However, at the concept design stage, relative stiffness is the important analysis factor for structure selection,layout scheme, the relationship between sub systems and vertical section.Calculation design and constitution design are constrained by code formulas and specific provisions; while concept design is qualified by basic principles and regulations. It is difficult to provide quantitative analysis on whether the concept design scheme is rational, or there is hidden defects or understanding deviation in the scheme.According to D'Alembert's equation,frequency and vibration modes are the inherent characteristic parameters only related to the mass and stiffness of the structure. Mode is effective tool of stiffness analysis in the preliminary design phase,which is independent of load cases and correlation to the layout, material property and geomety size of structure. Hence, evaluating the relative stiffness by modes can help carrying through quantification-aided design in concept design phase. At present,modes analysises are mostly used on dynamic characteristics of the structure. It is a promising subject to guide concept design by modes analysis.Supported by the National Natual Science Foundation of China(50978232) and the Foundation for the Exellent Doctoral Dissertation of Zhengzhou University, the thesis put forward deformation decompositon method of regular rectangle unite based on orthogonal theory. Major basic deformation can be obtained by this method to guide constitution design. This mtethod can also be utilized in the modes quantification identification, which can be used in quantification-aided design in concept design phase. The main results of the thesis are as follows:1 Complete rectangle orthogonal coordinate base has been built, to achive deformation decomposition of comprehensive deformation. Error analysis are carried out to verify the convergence and atabiliy. The results of deformation decomposition are compared to finite element analysis and experiment to validate the correctness.2 The assumption that the section is plane has been verified to forecast faliure modes of simple supported beams by deformation decomposition method. The predictable results can be used to guide constitution design of the stucture. The method also can separate vertical bending macroscopical deformation, which can be used to develop a strategy of plane steel members stability monitaring.3 Refined modes identification based on deformation decompositon has been proposed. The refined modes identification is achieved by extracting nodes relative displacements of one mode, proceeding deformation decomposition, obtaining propotion of every basic deformation. Results of the refined modes identification are compared to participation mass ratio method to validate the correcness and superiority.4 The refined modes identification method is used in modes identification of plane structures to identify some special modes types, such as shearing modes, local modes, shear-bending modes and bend-shearing modes. Columns types determination method is studied by analyzing modes characteristics of short, medium and long columns. Based on local modes, construction constrains of openings location of beams has been discussed. And shearing modes and local modes should be avoided in the concept design phase.5 Based on the refined modes identification method, coupled-shear coefficient has been introduced to study the deformation characteristic of shear walls. On foundation of present classification of integrated shear wall and coupled shear wall, a new type shear wall is proposed, whole coupled shear walls, which represents different mechanical characteristics under static and dynamic loads. So the whole coupled shear wall should be noticed in calculation design and constitution design,especially in seismic design. The mathimatical models for determining optimal design parameters of multistory and hign-rise buildings are eatablished, and optimationobjectives especially are the minimum of shearing deformaiton based zone proportion in basic mode, and optimum of ductility, lateral stiffness and bearing capacity.6 This thesis has explored the writing of general principles and subjects of plane structure concept design based on modes.Main contributions of the thesis are as follows.1 Complete rectangle orthogonal coordinate base has been built, to achive deformation decomposition of comprehensive deformation. In the case of small deformation, any deformation of a rectangle unite can be decoposed as eight basic displacement and deformation, such as rigid displacement, bending deformatin,tension-compression in x and y direction, shearing deformation and rotation displacement.2 Simple basic deformation modes can be decomposed by deformation decomposition, such as bending deformation and shearing deformation, to guide analysis,design and monitoring of strctures. Deformation quantization identication of simple supported beam can be relized by deformation decomposition method. The anticipation results can be used to guide constitution design of the stucture. The method also can separate vertical bending macroscopical deformation, which can be used to develop a plane steel members stability monitoring strategy.3 Refined modes identification based on the deformation decompositon has been proposed. Then some special modes has been identified, such as shearing modes,shear-bending modes, bend-shearing modes and local modes, which can help determine columns types. The refined modes identification is achieved by extracting nodes relative displacements of one mode, proceeding deformation decomposition,obtaining propotion of every basic deformation. The refined modes identification method is used in modes identification of plane structures to identify some special modes types, such as shearing modes, local modes, shear-bending modes and bend-shearing modes. Columns types can be determined, such as short, medium and long columns.4 Based on the refined modes identification method, coupled-shear coefficient has been introduced to study the deformation characteristic of shear walls. On thefoundation of present classification, a new type shear wall is proposed, whole coupled shear walls, which represents different mechanical characteristics under loads. So the whole coupled shear wall should be noticed in calculation design and constitution design, especially in seismic design. The mathimatical models for determining optimal design parameters of multistory and hign-rise buildings are eatablished, and optimation objectives especially are the minimum of shearing deformaiton based zone proportion in basic mode, and optimum of ductility, lateral stiffness and bearing capacity.5 The refined modes identification method are attemped to apply in concept design of structures, then quantitatively guide concept design. The foundation of concept design is the oveall control of relative stiffness.And vibration modes are the inherent characteristic parameters, which can be used to describe relative stiffness distribution characteristic. Hence, evaluating the relative stiffness by modes can guide quantification-aided design in concept design phase.