Sinusoidal Series Solution And Application Research On The Calculation Of The Deformation Of The Rod

In engineering structures or mechanical products,rod members or parts are one of the most commonly used and important components.For example,in the truss structure,the axially deformed tension and compression rods,the torsionally deformed shaft members in the transmission shaft,and the flexibly deformed beam members in the bridge.These members are subject to various constraints during design or use,such as hinged,fixed,or mixed constraints,and even undergo statically indeterminate constraints in order to meet their stiffness requirements.In addition,they will withstand various loads during use,such as static and dynamic loads,concentrated loads and distributed loads.When the types of rods are constrained,the types of loads and the number of loads are large,the traditional methods of unconstraining,force and integral methods will carry out a lot of problem analysis and mathematical processing in the process of use.And programming calculations are also very troublesome.Of course,as a numerical calculation method,the finite element method has been very successful in the treatment of rod deformation problems,but from the many literatures consulted,exploring and researching feasible theoretical calculation methods and ideas are still subject to people ’s extensive attentionIn view of the above problems,this paper proposes a solution to the sine series.This method is different from the existing deformation calculation methods.The calculation process is simple,convenient,and convenient to calculate,but the calculation results are consistent with the results of the existing deformation calculation methods.In order to prove the feasibility of this method,this paper analyzes the sinusoidal series solution of the axial deformation of the fixed rod at both ends,the sinusoidal series solution of the torsional deformation of the fixed shaft at both ends,the sinusoidal series solution of the bending deformation of the simply supported beam,and the hinged support The sine series solution of the deformation of the multi-span beam,the sine series solution of the steady-state response of the simply supported beams at both ends,and the sine series solution of the static response of the single lapped joint under axial force were studied and obtained.The series of analytical solutions to the problem is compared with the results of the unconstrained method and the integral method in material mechanics through calculation examples,which shows that the method is feasible and effective.In addition,the research ideas of the method in this paper have certain enlightenment and reference value for the deformation calculation of other constrained forms.