Deformation Reconstruction Of Array Antenna Truss Structure Based On Inverse Finite Element Method

As an important branch of ground-based radar,vehicle-mounted array antenna has the characteristics of large deployment span,high mobility,light weight,and high integration.However,it is also accompanied by some problems,such as the decrease of overall structural rigidity and easy deformation.,the electrical performance of the antenna deteriorates,etc.The above problems cannot be solved by increasing the structural stiffness through traditional conformal design.Therefore,it is necessary to use other means to monitor the structural deformation,and adjust the relevant parameters of the antenna according to the structural deformation,so as to improve the electrical performance of the antenna.Therefore,the key to improving the electrical performance of the antenna is whether it can accurately monitor the deformation of the truss structure of the front antenna.This paper focuses on the problem of deformation and reconstruction of the front antenna truss structure,mainly aiming at the singularity of the inverse finite element-like stiffness matrix,the inaccurate reconstruction caused by the selection of the theoretical model in the front antenna truss,and the position of the strain sensor.Corresponding solutions are proposed for the influence of the influence on the reconstruction accuracy,so as to complete the deformation and reconstruction research of the array antenna truss structure based on the inverse finite element.The main points of the full text are as follows:In the first part,aiming at the singularity of the stiffness-like matrix K in the traditional inverse finite element beam model,it is proposed to use the integral method to establish an inverse finite element mathematical model,so that the stiffness-like matrix K is always positive definite,and there is no need to consider the stiffness-like matrix in the subsequent optimization process.The singular problem greatly simplifies the solution process.Based on the Timoshenko beam displacement field theory,this part uses the integral method to construct the relationship between section strain and nodal degrees of freedom,and discusses the relationship between section strain and surface strain.The inverse finite element formula of the structure.The model of beam element is established,and the feasibility of deformation and reconstruction of beam model by the inverse finite element formula of element integration method is verified by simulation and experiment.In the second part,the displacement field under the classical beam theory is generalized and rewritten,so that the generalized displacement field formula can be applied to the two beam theories at the same time.Using the method of equivalent Young’s modulus,the Euler Bernoulli beam It is unified with the displacement and section strain expressions of Timoshenko beam theory,and the nodal degree of freedom solution matrix is determined by the unified nodal displacement and section strain expressions,so that the dimension does not change with the change of beam theory.In addition,finite element modeling simulation analysis and actual experiments are carried out on the Euler beam model and Timoshenko beam model to verify the universality of the unified inverse finite element method for the deformation and reconstruction of different beam models.The purpose is to solve the problem that the Euler beam and Timoshenko beam theoretical models are included in the front antenna truss structure,resulting in inaccurate reconstruction results and different matrix dimensions of the nodal degrees of freedom solution,which cannot be directly spliced.In the third part,the analysis of the stability of the strain sensor position layout is carried out.First,the influence of the strain sensor position on the deformation and reconstruction accuracy of the overall front antenna truss structure is discussed.Then,the objective function corresponding to the reconstruction accuracy index and robustness index is established,and the corresponding constraints are given,and the position of the strain sensor is optimized by using the multi-objective particle swarm optimization algorithm to obtain the optimal position.Finally,the applicability and stability of the strain sensor position optimization algorithm are verified by finite element modeling and simulation analysis of the rectangular beam.In the fourth part,the finite element model of the front antenna truss is established according to the classical front antenna truss structure picture,and the spatial coordinates of the nodal degrees of freedom matrix obtained by the deformation reconstruction formula of the element integration method and the unified inverse finite element formula are calculated.Conversion and element splicing are used to obtain the solution formula for the nodal degrees of freedom of the overall structure,and the overall optimization of the position of the strain sensor of each element is performed to complete the deformation and reconstruction of the truss structure of the front antenna.Effectiveness and accuracy of the deformation reconstruction method for antenna truss structures.