The State Space Theory of Engineering Structure Analysis and Its Pplications
|School||Hefei University of Technology|
|Keywords||structural analysis state-space method variation principle computer simulation engineering application|
The demand for structural analysis rapidly increases with the springing up of large and complex constructions. Presently, the study on theoretical method of structural analysis has experienced a fast development. As the characteristics of the State-space Method, it plays a very important role in the fields of construction, highway and bridge, water, machinery, environment and so on in the recent ten years. The State-space Method exhibits its strong superiorities especially on the mechanical analysis in these fields. Therefore, based on illustrating the limitations of the traditional analysis method, this paper introduces the application of the State-space Theory in the field of engineering structural analysis and points out the enormous advantages of it in the engineering structural analysis. Furthermore, self-views and analysis method are proposed, as well as the State-space Theory of engineering structural analysis is established according to the deficiencies of the traditional analysis method. The research in this paper covers multidisciplinary fields, which has accumulated experiences for future study.The main content is as follows:1. The establishment of the state equations. Choice the dual stresses and displacement components for state variables at first, and then construct the state-variable functions of the plane problems and the space problems, establish the state equations by the mathematical transformation and the Variation Principle.2. The new calculating theory and the method of static and dynamic response in complex structures. According to the static and dynamic control equations in different kinds of engineering structures, the finite element state equations are deduced by using the Hamiltonian Principle. The study calculates the finite element state equations by applying several calculating methods of modern control theory and the Finite Element Method of computational mechanics, and the responses of different kinds of statics and dynamics are acquired in engineering structural members during the application period.3. The Spline-state-variable Method is used to analyze the unified problems of static and dynamic responses in structures. (1). Based on the Instantaneous Variation Principle and the State-space Theory, a method which is called Simple-variable Spline-state-variable Method is established by using the spline functions to construct the dynamic displacement functions, it can analyze the unified problems of static and dynamic responses in structures. (2). Based on the Instantaneous Variation Principle, two kinds of dynamic functions namely displacement function and force function are independently constructed by using spline functions, so another kind of method which is called Multivariable Spline-state-variable Method can be established, it can simultaneously solve the unified problems on multivariable statics and dynamics in structures.4. The study on several calculating methods. The calculating methods, such as the reduced-order calculation on matrix index function, the iterative algorithm on state-space, the parallel algorithm on the precise algorithm and the high-order-matrix square are studied. They improve the solving efficiency and precision of the equations.5. The problem of how to solve the boundary conditions and the decoupling are studied. There are boundary conditions and initial conditions at the same time in dynamic problems. For initial conditions, the problems can be treated by solving the state equations. But it is difficult to treat the boundary conditions, for which need to decouple for the state-space field and the finite element field.6. The computer simulation of the State-space Theory on engineering structural analysis is established. Combined with the computer simulation, a new method on the study of structural system and structural members, the relationship of the computer simulation and the structural analysis is preliminarily studied. This paper also makes a further exploration for the depth and the width of the application of computer in structural engineering, and especially offers conditions for the large-scale simulation in complex structures.7. Based on the State-space Theory of engineering structural analysis which is established in this paper, the application and analysis of the theory in engineering are studied in detail, they mainly includes the response problems of thick and thin plates on elastic foundations, the stress problems of thick and thin wall multilayer pressure tube underground, the analysis of dynamic time-history response in plane-frame structures, the response problems of vertical dynamic on floors, the stress problems of structures in culverts, the stress and displacement problems in wall structures, the analysis of dynamic time-history response in high-rise structures, the response problems in arch and dam structures and so on. They sufficiently show the significance of the State-space Theory for the analysis of engineering structures.The application of the State-space Theory on the analysis of the static and dynamic responses in engineering structures, as a new theory system, is very less in domestic and overseas. Even in China, it is just at the initiation. So, it is a novel research direction in international and will have a wide development and application.