Study On Structural Dynamic Response Sensitivity Using The Approximation Theory Of Radial Basis Functions

The analysis for structural dynamical response sensitivity is generally used to assess the extent of the responses impact of the variation of structure parameters.And it is also such a significant part of structural dynamical optimization design.The degree of effect of design parameters on the dynamical responses can be determined,which can be regarded as a reference to improve the structural dynamic behaviors and to decide the modification direction for the best design.In the actual project,the analysis for structural dynamical response sensitivity plays an important role that direct effect the correctness of analysis result and the optimization of design in the constant problem that the structural dynamical responses as the optimize goal or constraint.Thus,it has great theory significance and utility value to research the numerical method for the analysis of structural dynamical response sensitivity.The current state of structural dynamical response sensitivity research is introduced.A new numerical method for structural dynamical response sensitivity is proposed on the basis of the method for structural dynamical response using the radial basis function approximation.And the optimization design for piled wharf structure is performed.The main contents of the research are as follows:1.A numerical method for solving dynamic response is constructed through combination of the radial basis function approximation and the collocation method.The proposed method can be used to calculate the jerk and the jerk equation,the three-order differential equation,adopting RBF interpolation to approach the real movement rule,which makes up the defect that the traditional methods can't be used to calculate the jerk.Aimed at the numerical characteristics of the differential equation,an improved RBF expression of joint interpolation combining the all-order derivatives of the variate is presented.And adding an initial-value condition whose order is equal to the differential equation's can obviously decrease the numerical oscillation.The results of the numerical examples indicate that the proposed method has the advantages of simple calculation process,high accuracy,and significant applicability to jerk equation.2.A numerical method for structural dynamic response sensitivity is proposed using the theory of the radial basis function approximation and the collocation method.And the computational programs are designed for calculating the dynamical sensitivities of displacement,velocity,acceleration and jerk.The comparison of the results of actual numerical example with the proposed method,precise integration method and difference method demonstrate the reliability of proposed method.Meanwhile,this method has the advantages of convenience of use and applicability of jerk sensitivity.Take,for example,the five-span spatial frame structure,the results of dynamical responses and the sensitivities respectively calculated by using the theory of Euler-Bernoulli beam and the theory of Timoshenko deep beam are compared.3.Structural optimization design is a great significant area applied the dynamical response sensitivity.Take an actual wharf structure for instance,aimed at the problems of analysis for structural dynamical responses and their sensitivity of the piled slab-beam wharf under ship impact load,a finite element model of “ship-rubber fender-wharf” is built.Then the proposed method in Chapter four is adopted to solve the structural dynamical responses and the sensitivities.The problem of wharf optimization design with the constraints of construction feasibility,the design variables of inclined pile slope and the optimization goals of dynamical response is solved.Finally,the vibration levels of the wharf under ship impact load is efficiently controlled.