The buckling behavior has an important effect on the performance of a dome structure. The computational time for the buckling problem will significantly rise, if a complex structure with considerable nodes and elements is concerned. This study develops an efficient method for the elastic stability for dome structures having high-order symmetry properties. Based on group theory, the elastic stiffness matrix and the geometric stiffness matrix are expressed in symmetry-adapted coordinate systems and decomposed into many sub-matrices. Then the eigenvalue buckling problem associated with the matrices is decomposed into many independent problems with smaller dimensions. To describe the general procedure for the proposed technique using the symmetry method, analyses on the stability of several highly symmetric dome structures are carried out. The results are compared to the corresponding ones obtained by the conventional numerical methods and using ABAQUS, to validate the computational accuracy. We will also prove the proposed method is efficient, by comparing the computational efforts with those cost by the other methods.
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