With sufficient precision, the approximate syminetrical destabilizing critical load for the circular arch with fixed supports are calculated by Ritz method.

This paper is based on the basic equation of polar coordinate solution in elastic planar problem,derived the state equation of planar problem of fixed arch,defined the displacement and stress triangular potential function, then obtained the accurate solution.

Based on the total potential energy of elastic curved beams by considering the geometrical nonlinearity, the theoretic solution for the flexural-torsional buckling load of fixed-end circular arches subjected to uniform compression and bending is deduced with the Retz method, taking the effects of warping rigidity into account.

In this paper,the non-linear dynamic governing equations of the generally laminated shallow arches are derived,the effects of geometric non-linearity ar considered but the effects of transverse shear are neglected.

he bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1:2 internal resonance is studied in this paper.

In this paper,the non-linear dynamic governing equations of the generally laminated shallow arches are derived,the effects of geometric non linearity are consided but the effects of transverse shear are neglected.