Hamiltonian Method For Bending,Torsion And Shear Hysteresis Analysis Of Composite Beam

Composite materials with high strength,good durability,good fatigue resistance and other aspects of good performance,therefore it can play a better role in many engineering fields such as civil engineering,machinery,aerospace and so on.Compared with the beam made of traditional materials,the beam made of composite materials has more advantages in mechanical properties and economy,so the research on its mechanical properties is particularly important.At present,there are a lot of research achievements on the mechanical properties of composite beams,but there are few literatures introducing the solution methods.Based on this,in this thesis,functional gradient beams and fiber composite thin-walled box beams were taken as research objects,under the Hamiltonian mechanics system,the curve of functionally gradient beams,transverse force hysteresis and transverse transformation of fiber composite thin-walled box beams and bending and torsion coupling problems were studied.The Lagrange system of the structure was firstly derived by using the energy variational principle,and then the dual variables were introduced through the Legendre transformation,so the Lagrange system was introduced into the Hamiltonian system,the Hamiltonian methods for the analysis of bending,torsion and shear hysteresis of composite beams were proposed.The solution of high-order differential equations were avoided and the difficulty of solving was reduced.At the same time,the precise integral method has the advantages of easy convergence,fast speed and high precision.The main contents are as follows:(1)For functionally graded beam bending,the thesis was based on the first-order transverse transformation theory and the theory of Hamiltonian,three generalized displacements were selected as unknown functions,the bending analysis model of functionally graded beam was established,to study the different terminal conditions and high span ratio and different volume fraction index of beam under transverse and longitudinal displacement,stress spread on cross section,and the influence of elastic modulus ratio on vertical displacement;(2)For the transverse force hysteresis and transverse transformation of fiber composite thin-walled box beam,based on Hamiltonian mechanics and composite laminated plates theory,four generalized dispositions were selected as the basic unknowns.A new theoretical analysis method which can consider various coupling effects was proposed to analyze the shear hysteresis effect of fiber composite thin-walled box beam.And the correctness of the proposed method was verified by the experimental results and the calculation results of other methods;(3)For the flexural and torsional coupling problem of fiber composite thin-walled box beam,based on Hamiltonian theory,laminated composite plate theory and thin-walled bar theory,the effect of secondary shear stress on constrained torsion was considered,and the twist rate in the displacement field was replaced by the warping function.Seven generalized displacements were selected as the basic unknowns to represent the displacement field of the bent-torsion coupling of the laminate box beam,and the effect of limiting warping was considered,a flexural and torsional coupling analysis model of fiber composite thin-walled box beam was established.The validity of the model was verified by comparing the calculation results with those of the existing methods.Therefore,it provided a new idea for this kind of structure analysis.