Equivalent Model Research Of Variable Section Beam Based On Energy

With the rapid development of engineering technology,in the design process of bridges,buildings and aerospace,more and more variable-section beams have been widely used because the equal-section beams are difficult to meet the strength requirements.However,the governing equation of the variable section beam is a variable coefficient differential equation.The approximate solution is generally used to solve the model,and it is difficult to obtain a high-precision solution.According to the structural characteristics of variable cross-section beams,based on the energy equivalent method,this paper studies the equivalent model of variable cross-section beams,which brings great convenience to the follow-up optimization work.Firstly,this paper discusses the research background and significance of variable cross-section beams,the research status at home and abroad,and the key technologies and difficulties in swing arm.Based on Timoshenko beam theory and Euler-Bernoulli beam theory,appropriate methods and basic parameters are determined,which lays a good foundation for deriving and verifying the equivalent multi-modal model of variable crosssection beams.Secondly,based on the principle of strain energy equivalence in energy method and Euler-Bernoulli beam theory,the beams with different cross-sections are modeled and the element stiffness matrix and mass matrix of circular,rectangular and trapezoidal beams are derived respectively.The derivation process is mainly to obtain the cross-section parameters by Lagrange interpolation function,then calculate the equivalent moment of inertia by using the Gauss integral quadrature method,and substitute the equivalent moment of inertia into the stiffness matrix and the mass matrix of the beam with equal cross-section,so that the stiffness matrix and the mass matrix of the beam with variable cross-section can be obtained.The three-dimensional model of variable cross-section beam is built in SolidWorks software and imported into ABAQUS.The stiffness matrices of different cross-sections are verified separately.The simulation results and theoretical errors of different variable cross-section beams are compared.At the same time,the stiffness matrix of the beam with variable cross-section based on the energy method is verified by the simulation calculation by applying the motion pair and driving to the model built in ADAMS software and applying a linear change force from zero to 100 N at the right end of the bar.Then,on the basis of structural modal analysis theory and vibration theory,the equivalent model of variable cross-section beam is studied,and the equivalent stiffness formula of variable cross-section beam element is applied to the equivalent rigid body model.At the same time,the modals of equivalent rigid body are calculated by MATLAB programming,and then discrete analysis is carried out by ADAMS software.The pendulum arm is discretized into multi-segment rigid body model.The rigid body model is flexible by discrete equivalent nodal connection force,and the equivalent load is applied between each rigid body.The ADAMS program code is compiled by the model,and the modal and finite element accuracy of beam element models with different cross-section under different size parameters and different discrete points are analyzed.The finite element software analysis results of the two methods are compared.The results show that the finer the beam model is discretized,the higher its accuracy will be.