Beam Theory Considering Cross Section Deformation And Its Application In Wing

During the period of wing structure design and strength analysis,the establishment of wing finite element model is an indispensable step.At present,the commonly used models are the "plate-beam" model and the equivalent beam(or plate)model.However,the "plate-beam" model is complicated and time-consuming,especially in the initial design and the dynamic analysis of the wing,while the equivalent finite element model relies on the engineering experience,and the accuracy is limited.For the high-aspect-ratio wing,the wing components are mainly slender members.In this paper,the beam element is used to model skin,wing spar,stringer and some other structures,and the traditional beam elements are obviously unable to complete the work.To this end,this paper presents a high-precision three-dimensional beam model based on cross-section interpolation,which considers in-plane deformation and out of plane deformation and can be used to model any slender components.Firstly,the cross-section interpolation function—Lagrange function is introduced to describe the cross-section shape,and the displacement vectors are used as unknown variables to describe the displacement of the cross-section.On this basis,the displacement field of the beam element is constructed according to the interpolation theory.Then,the stiffness matrix and mass matrix of beam element are given based on the virtual work theory.At the same time,the discrete method of cross section of complex structure is given and the corresponding finite element programs of preprocessing and postprocessing are compiled by MATLAB.Based on this,a solid beam,a thin-walled open beam and a thin-walled closed beam are used as typical examples to validate the reliability and the advantages of the beam element through the comparisons with the traditional beam element and the solid element of Nastran.Finally,the finite element model and static and dynamic analysis of a long straight wing structure are carried out using the beam element,which provides a one-dimensional beam simplified modeling method for the design and analysis of long straight wing structures.