Overestimation Research And Bandgap Analysis Of Uncertain Structures

Due to the uncertainty of material physical parameters,external excitation,boundary constraints and processing assembly errors,the static and dynamics and their response of engineering structures are often difficult to predict accurately.For complex structures,uncertainty can lead to unreasonable results,which may have a serious impact on the project.At present,it is necessary to carry out research on the static and dynamics analysis of uncertain structures by considering the uncertain factors and combing with the actual problems of engineering.In this paper,the uncertain structure is taken as the research object,the overestimation phenomenon and bandgap analysis are separately analyzed.1.The shape-finding design of uncertain structures based on interval force density is studied.Aiming at the overestimation problem of static of interval force density algorithm,an improved interval truncation method is introduced to eliminate it,and an improved interval force density algorithm for cable net structure is proposed.The algorithm is applied to the shape-finding optimization design of the uncertain cable network structures.To establish the shape-finding optimization model,the force density is defined as design variable,the shape accuracy of the reflection surface is defined as objective function,and the longest cable segment is defined as constraint condition.The examples show that the improved interval force density algorithm effectively solves the overestimation of static and is suitable for shape-finding optimization design.2.The dynamic analysis of interval finite element based on uncertainty structure is studied.Aiming at the overestimation problem of interval finite element,the structural dynamic response is taken as the model,and the element-based sub-interval perturbation method is introduced to eliminate it and break the limitation of interval parameter range.The dynamic model based on interval finite element is modified by introducing Laplace transform.The structural dynamic response is solved by Laplace transform and Laplace inverse transform,which makes the solution process convenient and reduces time-consuming.The examples show that the proposed method effectively solves the overestimation problem of interval finite element of dynamics analysis.The method is not limited by the range of interval parameters and takes less time in the solution process.3.The bandgap properties of periodic structure based on uncertain structures is studied.Therefore,for the bandgap properties of the periodic structure,the bandgap equation of the two-dimensional lattice in the unit cell containing different numbers of atoms is derived by introducing the finite element method and combining the bloch theorem.Considering the uncertainty of the periodic structure,the perturbation and the asymptotic integration methods are introduced respectively.The uncertain structure is taken as a linear stochastic system,the wave number is taken as a constant,and the spring stiffness and mass are taken as random variables.The relationship between the wave number and the natural frequency is analyzed to obtain the map of bandgap properties.Furthermore,the failure condition of the Bloch theorem and the influence of the uncertainty of mass and spring tiffness on the bandgap properties is further studied.The examples show that the proposed method effectively solves the problem that the uncertain periodic structure is difficult to solve the bandgap properties within a certain range.