Nonlinear Mechanical Modeling Of Preloaded Jointing Structures

Complex structure systems such as jet engines,aircrafts,automobiles and weapon systems are commonly assembled with different parts and components.A typical missile consists of four main components as warhead,engine,guiding system and body.Each component consists of large amounts of parts.Different jointing techniques are applied between part-to-part,part-to-component and component-to-component.Under external forces,complicated micro and macro slipping occurred on the contact interfaces are responsible for influencing the dynamic behaviors of the build-up structures.They are also the main cause of stiffness nonlinearity,damping and energy dissipation.It is shown that energy dissipation caused by micro and macro slipping are the main source of structure damping,which accounts for 90%of the total damping.During the dynamic analysis of complex build-up structures,DNS(direct numerical simulation)method is unavailable due to the limitations of huge computing scale and small timing step.Taking the jet engine as an example.A typical jet engine may have the length scale of meters while the contact elements of the finely meshed model are at the length scale of 10-5m.What's more,the computing time till steady state of the problem may last for seconds while the explicit timing step for the problem are nanoseconds.Due to these two main obstacles,the computing scale and total timing steps are so large that the simulation becomes intractable.Therefore,investigating the nonlinear properties of contacts,establishing theoretical models for the nonlinear mechanism and reducing the computing scale and total timing steps for these problems are of great importance.The contact problems of joints,which are widely applied in complex build-up structures,are discussed and investigated in this paper.A constitutive model for the nonlinear behaviors of contacts are proposed.Theoretical derivation and numerical simulation of the proposed model are carried out.Experimental approaches of jointed structures are also performed.Contents of this paper are listed as below.A modified energy dissipation model is established based on Goodman's energy dissipation model for flat lap structures.The proposed model can be used to reflect the experimental results of the power-law relationship and can also be degraded into Goodman's model in a certain condition.A six-parameter Iwan model that contains a truncated power-law distribution with two Dirac Delta functions is established based on Segalman's four parameter Iwan model and Song et al.'s modified Iwan model.The analytical expression of backbone curve,unloading curve and energy dissipation of the proposed model are deduced.Parameter identification method of the model are also provided.According to the stiffness equation,four discretization methods including arithmetical discretization based on displacement,geometrical discretization based on displacement,arithmetical discretization based on stiffness and geometrical discretization based on stiffness are provided.Numerical simulation of an SDOF oscillator is carried out to discuss the influences of different numbers of Jenkins elements and discretization methods on the computing accuracy of jointed structure.Quasi-static and dynamic experiments of bolted joints are performed to investigate the influences of contact surface roughness,preloading and bolt arrangements on energy dissipations and force-displacement relationships of joints.Nonreversible wear and damages are found on contact interfaces of test specimens after repeated loadings,which leads to a markedly decrease of bolt preload.Rougher contact surfaces make more energy dissipation.Higher bolt preload makes less energy dissipation.With the same bolt preload,more bolts make the dissipated energy even higher.When the number of bolts is fixed,test specimen with series bolt arrangement dissipates more energy than that with parallel bolt arrangement.Experiment results of force-displacements indicate a larger macro slipping force with larger bolt preload.A peak value of applied force can be found in force-displacement curve at the transition of micro and macro slipping.After that,the applied force drops to a certain value and macro slipping occurs.An assembled structure containing a thin walled cylinder with three single-bolted connections is designed.Sine-wave frequency sweeping and fixed frequency exciting experiments are performed.Finite element modeling of the thin walled cylinder is carried out with connections represented by discretized six-parameter Iwan model.Experiment results show that the resonance peak drifts to lower-frequency direction with a higher excitation magnitude,which also leads to stiffness softening of the assembled structure.With a higher excitation frequency,acceleration results of different test points on thin walled cylinder are magnified to some extent.In the circumstance of low excitation frequency,calculated and experimental results at z direction of the four test points on the top of thin walled cylinder match well with each other.Accelerations are magnified when frequency increases,which leads to a less computing accuracy.Applicability study of the six-parameter Iwan model is carried out.First,a finite simulation of flat lap joint with modified friction model is performed.The six-parameter Iwan model is identified according to the calculation results.Then a discretized numerical simulation is carried out.Good conformities can be found between the calculation results of modified friction model and discretized Iwan model.After that,the applicability of the proposed model is further discussed according to the quasi-static and dynamic experiment results.It is shown that the power-law relationship of Goodman's model is 3.0,which cannot precisely reproduce the experiment results.The power-law relationship of the proposed energy dissipation model based on modified friction model for flat lap structure is 2.754,which matches well with the experiment results 2.786.Calculated and experimental results of energy dissipation also show a good conformity.The proposed energy dissipation model for flat lap structure can be used to precisely describe the energy dissipation properties of flat lap structure.Residual stifness can be found on contact interface during macro slipping stage and the power-law relationship is between 2.4 to 2.9.The proposed six-parameter Iwan model can precisely describe these two phenomena at the same time.Compared with other three discretization methods,the geometric discretization based on stiffness can provide a higher computing accuracy.The identified Iwan model matches well with experimental results under different conditions.The six-parameter Iwan model can precisely describe the nonlinear behaviors of bolted joints.