Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory（CPT）, the first-order shear deformation plate theory（FPT） and the Reddy＇s third-order shear deformation plate theory（RPT）, analytical relations between the eigenvalues of circular plate based on various plate theories are investigated. In the present paper, the eigenvalue problem is transformed to solve an algebra equation. Analytical relationships that are expressed explicitly between various theories are presented. Therefore, from these relationships one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions. The relationships are useful for engineering application, and can be used to check the validity, convergence and accuracy of numerical results for the eigenvalue problem of plates.
One purpose of this paper is to give a brief overview on the research status of deformation,fracture and toughening mechanisms of polymers,including experimental,theoretical and numerical studies.Emphasis is on the more recent progresses of micromechanics of rubber particle cavitation and crazing,and the de- velopment of fracture criteria for ductile polymers. The other purpose is to study the effect of triaxial stress constraint on the deforma- tion and fracture behavior of polymers.Polycarbonate(PC),acrylonitrile-butadiene- styrene(ABS)and PC/ABS alloy are considered in this investigation.A series of circumferentially blunt-notched bars are used to experimentally generate different tri- axial stress fields.The fracture surfaces of specimens with different notch radius are examined by scanning electron microscope(SEM)to study the fracture and tough- ening mechanisms of polymer alloy.It is shown that the triaxial stress constraint has a significant effect on the deformation,fracture and toughening of PC,ABS and PC/ABS alloy.We will also discuss the extent to which a micromechanies criterion proposed by the first author can serve as a fracture criterion for ductile polymers. A new ductile fracture parameter is emphasized,which can be employed to evaluate the fracture ductility of polymers.Stress state independence of the parameter for the PC,ABS and PC/ABS alloy has been experimentally verified.
