| Cylindrical orthogonal single-layer lattice shell structures intersected by two cylindrical shells are new type shell structures. The determinant of design of single-layer shell structures is stability but not lied on strength. At present, researches about the static behavior and geometrically nonlinear static stability of cylindrical orthogonal single-layer lattice shell structures have been consummate. But as to geometrically nonlinear dynamic stability of the structure under the earthquake loads, the researches are in the beginning. Based on nonlinear finite element theory, the tangent stiffness matrix in space frames is deducted and the program of nonlinear dynamic stability is compiled. The acceleration values of seismic loads are adjusted by proportion method, so that the peak value of acceleration answer calculation needs. The dynamic responses of cylindrical orthogonal single-layer lattice shell structures supported on the rigidity beam and at four corners are calculated under seismic loads of different acceleration. So the displacements of joints of the shell structures are got and the maximal nodes displacement of the all structures can be found. The curve of maximum displacement of nodes under dynamic acceleration and curve of displacement history of the nodes of shell structures can be drawn, the dynamic stability critical loads of cylindrical orthogonal single-layer lattice shell structures is estimated thought Budiansky-Roth rule, the curve of node displacements time history and the configuration of the shell structures. At the same time, in the paper dynamic stability of cylindrical orthogonal single-layer lattice shell structures are analyzed considering different structural parameter, for example the section of the members, ratio of rise to span etc. Some useful conclusions for the seismic resistance design are given for the engineering, and some questions of the structure that should be resolved in the future are discussed.
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