Wind-resistant Optimization Design Of Lattice Tower Structure With Linear And Geometrical Non-linear Analysis

As lattice tower structure normally has the larger slenderness members and obtains the feature of lightweight, high flexibility and small damping ratios, so it is easy to behave with large displacement and to collapse due to instability under wind load. At present, the wind-resistant design of lattice tower structure mianly relies on the experience of the engineers and linear elastic analysis method with the consideration of length-to-slenderness ratio by repeated trial design. Although the final design is feasible from the design code view, the designed cross section size is not always the optimal results. Taking a lattice tower as an example, non-stationary analysis and numerical simulation on time history of stationary fluctuating wind speed was conducted firstly in this paper, the random vibration analysis of wind-induced response and equivalent static wind load of the lattice tower was then obtained. Meanwhile the design sensitivity analysis of wind-induced response(including displacement, stress, critical load factor etc.) with respective to the optimized design variable was investigated by static linear and geometric nonlinear analysis procedure. By adopting the modified Optimality Criteria(OC) structural optimization algorithm and the SAP2000 Application Programming Interface(API) developing enviorment for MATLAB, an automic wind resistant optimized design procedure for lattice tower structure was proposed in this thesis by linear elastic and geometrical non-linear analysis on the investigated lattice tower, the main research aspects were specified in the following:1. Non-stationary analysis was conducted on the measured wind speed by Empirical Modal Decomposition(EMD) method, a three-dimensional non-stationary wind model was proposed by considering the coupling effect of wind speed and direction in this paper. Some new variables related with wind characteristics, such as the time-varying standard deviation and time-varying turbulence intensity, were proposed in this paper. In order to verify the accuracy of the proposed method, the field measured wind data from a typhoon was selected to investigate its non-stationary characteristics comprehensively by comparing with the traditional data analysis, and the results showed that the proposed model has better accuracy.2. Numerical simulation of random fluctuating wind speed was conducted by Constant Amplitude Wave Superposition method(CAWS). Some parameters related with wind characteristics, such as the autocorrelation coefficient, cross correlation, turbulence intensity and power spectral densities were furthermore compared for the numerical simulation results with the target value. Time history record of the simulated fluctuating wind was obtained with good accuracies. At the same time, the parallel computing architecture with multi-processcore platformwas adopted to improve the computation speed.3. The random vibration analysis of wind-induced response was conducted and the equivalent static wind load(ESWL) was computed by Harmonic Excitation Method(HEM) and POD-Ritz method. The vibration modes were obtained by Proper Orthogonal Decomposition(POD) on fluctuating wind vector and the load-dependent Ritz vibration analysis.4. The design sensitivity analysis of wind-induced response(including node displacement and stress in the element) with respective to the design variables were investigated by the inverse process of the finite element analysis procedure. Considering the unique feature of the element tangent stiffness matrix for the three dimensional beam in the geometrical non-linear finite element analysis procedure, the analytical formula for design sensitivity of nodal force in the finite element model was proposed in this thesis by adopting the finite element analysis results from SAP2000 software. Furthermore, the design sensitivity analysis of node displacement and stress in the element were obtained by utilizing the design sensitivity results of nodal force in FEM model. At last, the accuracy and effectiveness of the proposed formula were verified by comparision of theoretical solution with and the proposed method on a flat three-bar truss structure.5. The methodology and principles of "one-point approach" and "two-point approach" for predicting the nonlinear critical load for space structures were firstly investigated in the thesis. Then the design sensitivity analysis of nonlinear critical load factor with respective to design variable were proposed by utilizing the design sensitivity results of nodal force in FEM model. The accuracy of proposed method for the nonlinear critical load factor was also verified by taking a dome truss structure as the example.6. In aspect of wind-resistant structural optimization procedure, the computational principles of Optimality Criteria(OC) were comprehensively introduced. Some modification on the solution algorithm for the Lagrange multipliers in the optimization procedure was proposed for more efficiency and accuracy. The modified Optimality Criteria algorithm was demonstrated for a simple cantilever column structure as an example to verify its accuracy.7. Finally utilizing the corresponding algorithms proposed in the previous chapters, a comprehensive wind-resistant optimization design procedure for a lattice tower structure were proposed by modified OC method and adopting SAP2000 API for static linear and geometrical non-linear finite element analyzed results of this structure. With the simultaneous satisfication of the constraint on the wind-induced node displacement, stress in the element and nonlinear critical load factor for the whole lattice structure, the minimum total weight(or cost) of the whole lattice tower was obtained by the comprehensive wind-resistant optimization algorithm. The updating on the time history of fluctuating wind acting on the tower structure and its corresponding equivalent static wind loads(ESWLs) were seamlessly integrated in the optimization procedure. The wind-resistant optimized results for this tower structure under various loading cases were studied in a great detail at the latter part.