Research On Nonlinear In-plane Elastic Buckling Of Laminated Composite Arches

Composite laminated arch is a kind of component which takes a single-layer arch as basic unit and is arranged according to the fiber direction and stacking sequence after thermofixation process.It has been widely used in civil,mechanical,aerospace,and marine engineering owing to its outstanding performances such as light weight,high strength,corrosion resistance and easy forming.As a typical compression-bending member,the laminated arch may collapse abruptly under the action of external force.Since there is no obvious sign prior to buckling,major safety accidents may happen once the buckling occurs.As a result,the buckling should be strictly avoided in practical engineering.In recent years,it is found that the buckling of the laminated arch also has a positive side,some devices such as piezoelectric actuator,liquid pumping,energy acquisition,and energy dissipation damper have been invented utilizing the bistability property which overturns the conventional understanding about the buckling.Therefore,it is of great importance to accurately explore the buckling characteristics of the composite laminated arch for passive defense avoiding risks and active excitation for proper use.The laminated arch has an obvious anisotropic characteristic which is different from the isotropic counterpart.Due to the existence of the compression-flexure coupling effect,it is difficult to determine the corresponding buckling load.This thesis,therefore,carried out systematic research on the nonlinear in-plane buckling of the composite laminated arch having different section types,loading schemes,and boundary conditions by using a combined analytical,numerical,and experimental method.The main content includes:(1)The nonlinear buckling analysis method of a laminated arch with square section is put forward.According to the composite mechanics,the elastic stiffness matrix in the non-principal elasticity direction is derived.Governing equations for fixed and pinned laminated arches under a central concentrated load are built about the neutral plane,from which the analytical buckling load are obtained.The equilibrium paths of the arches are traced while a key equivalent modified slenderness ratio parameter is defined to characterize the buckling modes.The effects of ply-angle,included angle,and slenderness ratio on the buckling load are discussed in detail.Furthermore,the necessity of considering shear deformation is clarified.A general theoretical framework for the medium-slenderness-ratio arch is established based on the Timoshenko shear deformation theory.(2)The analytical solution for the buckling of laminated arches under an arbitrary radial point load is presented.To qualitatively describe the load offset level,the Dirac delta function is introduced into the derivation.The relationship between loading position and buckling behavior is revealed.An automatic displacement loading device is customized,field tests are carried out to verify the accuracy of the presented analytical solution.By using the loading device,the nonlinear equilibrium paths for laminated arches with different rise-to-span ratios,layer-ups,and loading positions are followed.Subsequently,the buckling configurations corresponding to the upper and lower limit point are captured by recording the complete buckling evolution processes.(3)The nonlinear in-plane buckling behavior of an angle-ply laminated arch with I-profile is explored.A parallel axis theorem is served to accumulate the stiffness of webs and flanges and the elastic stiffness matrix of the arch is established accordingly.For the convenience of analysis,a neutral plane concept is employed to decouple the internal forces.The critical buckling loads of the arch with fixed,pinned,and pinned-fixed ends under a uniform radial loading are determined,with an assumption that the axial force during buckling being a constant.Finally,the deformation characteristics and the internal force distributions of the laminated arch are described.The effects of boundary condition on the buckling pattens and buckling loads are thoroughly researched.(4)The theoretical analysis model for an elastic supported arch with orthotropic laminated box section is established.According to the principle of stationary potential energy,the functional expressions for the displacement and load conditions of linear and rotational elastic supports are given.The relations between restraint flexibility and the lowest modified slenderness ratio for bifurcation buckling,the critical modified slenderness ratio between bifurcation and limit point buckling,and the lowest modified slenderness ratio for limit point buckling are established.Subsequently,the similarities and differences of the buckling behaviors for laminated arches with elastic and ideal boundary conditions are shown.The buckling trends for the laminated arch with linear elastic supports under uniform radial loading and that with rotational elastic support under a central concentrated load are found.(5)The buckling mechanism of an orthotropic laminated arch with box section exposed to a uniform thermal environment is revealed.The thermoelastic behaviors of the arch are studied firstly based on a linear strain theory.Then,analytical solutions for the internal forces,axial displacements,and support reactions are obtained.After that,the governing equations for the laminated arch under a uniform radial and thermal loading are built considering the nonlinear deformation effect prior to buckling.The critical buckling load of the arch is solved.Meanwhile,the critical modified slenderness ratio under different thermal parameters is determined.Finally,the influences of the uniform temperature rise on the buckling behaviors for the laminated arch are discussed from both a macro and micro perspective.