Stochastic Analysis And Optimization For Dynamic Interaction Between Vehicles And Road/Bridge Structures

With the rapid development of national economy, railway and highway transportations are getting increasingly busy. Higher speeds and heavier loads of the vehicles have caused the dynamic interactions between vehicles and road/bridge structures received much attention. As the dynamic impacts applying on the supporting (road or bridge) structures by moving vehicles affect the working status and service lives of these structures significantly; and the running smoothness and safety of vehicles have become the main factors in evaluating the reasonability of structural design parameters, therefore a comprehensive research of the interactions between vehicles and road/bridges are of great importance for their design and construction. The vibrations of vehicles and road/bridge coupled systems induced by road irregularity are essentially random, but the research work associated with such random vibration has not been well developed because of the high complexity and cost of conventional methods for random vibration analysis. Up to date, not much research work on vehicle-road/bridge system random vibration can be found in the literature. In the present thesis, some advanced computational mechanics methodology, including the pseudo excitation method (PEM) for random vibration, the precise integration method (PIM) for time history integration, etc, are introduced into the present research on dynamic analyses and optimum of various coupled vehicle and supporting structure systems based on the theoretical framework of random vibration. Furthermore some innovative schemes based on the above methodologies have been developed, which can be summarized as follows:1. Vertical random vibration analysis of vehicle-pavement coupled systemsFor vertical random vibration analysis of vehicle-pavement (or road) coupled system, the two-dimensional moving element method (MEM) is derived by using a coordinate system which moves with the vehicle. The pavement elements are regarded as conceptual elements that'flow'with the moving vehicle along the pavement in this coordinate system, and vehicle is static. It is never necessary to cross from one element into another, which avoids the updating of force or displacement vectors due to change of the contact point with the elements. It can be found that the element stiffness and damping matrices thus easily obtained are simply a revision of the corresponding static element stiffness and damping matrices by superposing the terms with the velocity, foundation parameter and other coupled effects. So the non-stationary random vibration can be transformed conveniently into a stationary one, and it is accurate and efficient.2. The sensitivity analysis and optimum for vehicle stationary random vibration The complicated analysis process and costly computation efforts are always the mainly difficulties for the random vibration optimum design based on conventional methods, which lead to the difficulty of the random vibration sensitivity analysis. In this thesis, an accurate and efficient sensitivity analysis formula for optimizing the ride comfort of vehicle suspension system is derived. Based on the dynamic responses analysis using PEM, the random equations of motion with the right-hand side random acceleration is replaced by a pseudo acceleration excitation, thus various first and second orders of sensitivity formulas are calculated conveniently by differentiating these equations. Using the method the random dynamic sensitivity analysis is transformed into a deterministic one, and the optimal solutions when vehicle ride comfort is the objective function are derived by means of these flexibilities. The optimization efficiency and the computational accuracy are numerically justified.3. Multi-objective stochastic dynamic optimum design for vehicles based on simulation technologyIt is particularly unacceptable for stochastic dynamic optimum of structures in practical engineering field, which requires usually many re-analyses and complicated analyses process. Especially to multi-objective optimum, the unified and efficient sensitivity analysis method applied to the objective functions has not been well developed. In this thesis, the Kriging model is extended to vehicle multi-objective optimum problems, a method of filled function is set up to build the approximate mapping relationship between the design variables and the responses, and the random responses analysis is performed using the filled function instead of the objective function, with necessary modification for the filled function in every step to keep the precision. The optimization efficiency is thus enhanced remarkably by avoiding too many re-analyses. The multi-objective function is processed by means of the method of centers, i.e. by self-adaptively introducing an upper bound on each objective function that forms the level sets of the objective functions, and repeatedly calculating the center of the intersection sets consisting of the original constraint sets and the level sets of the objective functions.4. The random vibration analysis and optimum design for vehicle-bridge coupled random vibrationFor dynamic analysis of vehicle-bridge coupled system, the PEM has been applied to transform the random surface roughness into the superposition of a series of deterministic pseudo-harmonic surface unevenness. The PIM has also been extended to simulate the continuous variation of the contact forces, both in their magnitudes and positions, within each time step. As a result, the solution of the uniformly modulated, multi-point, different-phase, non-stationary random vibration can be obtained efficiently by means of PEM-PIM. An innovative method (PEM-PIM Based Sensitivity) for first and second order sensitivity analyses of structural random responses is developed based on PEM-PIM. For the random equations of motion, by replacing the right-hand side random excitation by the pseudo-excitation, various first and second order sensitivity formulae can be derived conveniently and accurately.5. FEM-based random vibration analysis and associated mechanical behaviors study of vehicle-road/bridge coupled systemsThis subject is concerned with many problems, including random vibration analysis, stochastic dynamic optimum and fatigue life estimation, and so on. Analysis of such random vibration mechanical behaviors has long been regarded as very difficult, particularly if finite element models with many degrees of freedom are used. Optimum design is even more difficult although it is of great concern and significance. To overcome these difficulties, some advanced computational mechanics methodology, such as PEM for random vibration, PIM for the numerical integration in the time domain or space domain and some efficient sensitivity analysis methods are used in this paper to study the random vibration mechanical behaviors in the vehicle engineering field. Some useful results about structure random fatigue life, vehicle dynamic impact influence and structure random dynamic optimum are obtained, and the efficiency and computational accuracy of the proposed methods are justified.