Flexural-torsional Buckling Of Circular Arches With Monosymmetric Section

In practical engineering,the section types of arch are various,including the biaxial symmetric and monosymmetric sections.At present,the theory of flexural-torsional buckling of arches with monosymmetric section is immature,associated with the unclear buckling mechanism and the lack of design basis.It is difficult to explore the flexural-torsional buckling of arches with monosymmetric section as the centroid of the section does not coincide with the shear center although the flexral-torsional buckling of the arch occurs around the shear center.In case of establishing the energy equation of flexrual-torsional buckling of the arch,the parameter items reflecting the monosymmetric section will be added,which make it more difficult to obtain the buckling load.Therefore,in order to improve the flexral-torsional buckling theory of arch with monosymmetric section and reveal its flexural-torsional buckling mechanism,a series of studies on the flexrual-torsional buckling of circular arch with monosymmetric section made of homogeneous material and graphene platelets reinforced porous material under complex load,are carried out in this paper as follows:(1)Based on the Timoshenko's principle,introducing the coordinate transformation matrix and the curvature matrix,the expressions of strain function including the effect of shear deformation are derived for the flexral-torsional buckling analysis of arches with monosymmetric section.Moreover,the formulas for calculating the positions of effective centroid and shear center of monosymmetric section are determinated.The expression of monosymmetric parameter in flexural-torsional buckling energy equation of arch is constructed.(2)The pre-buckling exact internal forces of circular arch with monosymmetric section made of isotropic homogeneous material under arbitrary radial concentrated load and localized uniform radial load are solved respectively.Subsequently,the energy equations for the flexral-torsional buckling of circular arch with monosymmetric section under external loads are obtained,and the theoretical solutions for the flexural-torsional buckling load are then derived by the energy method and Ritz method.In addition,the theoretical solutions are verified by the finite element software,and the effects of shear deformation,monosymmetric parameters,load position and slenderness ratio on the buckling load are analysized.(3)In the temperature gradient field,the theoretical solutions for the flexural-torsional buckling loads of isotropic homogeneous circular arch under arbitrary radial concentrated load and localized uniform radial load are derived respectively.The variation principle of buckling load with the temperature difference is revealed.It is found that when the absolute temperature difference is the same,if the lower flange temperature is smaller than the upper flange temperature,the flexural-torsional buckling resistance of the arch will be reduced.In the temperature gradient field,the effects of flexibility parameters,slenderness ratio and shear deformation on buckling load are different from those at ambient temperature.(4)The effective elastic modulus of graphene reinforced composites was determined by Halpin-Tsai micromechanical model.The flexural-torsional buckling loads of graphene reinforced functionally graded porous circular arch under arbitrary radial concentrated load and localized uniform radial load are deduced respectively.Then the correctness of the theoretical solution for the buckling load is verified by finite element software.Finally,the effects of pore distribution type,porosity coefficient and graphene weight fraction on the buckling load are discussed.It is found that the buckling load can be effectively improved by using a low content of graphene to reinforce the porous material arch.(5)The flexral-torsional buckling of graphene reinforced functionally graded porous circular arch is studied under the uniform temperature field as well as the combine action of the uniform temperature field and central radial concentrated load.The flexral-torsional buckling temperature difference and load are determinated by the Ritz method accordingly.The influences of pore distribution type,porosity coefficient and graphene weight fraction on the buckling temperature difference and load are analyzed.It is found that the buckling temperature difference of monosymmetric porous arch under the uniform temperature field increases with the increase of porosity.