New functional for hyperbolic paraboloid shell using refined field equations and a mixed FE solution


Teknik Dergi/Technical Journal of Turkish Chamber of Civil Engineers, vol.9, no.DEC., pp.531-535, 1998 (Scopus) identifier


Using tensorial field equations of shells a new functional for shallow hyperbolic paraboloid (hypar) shells, suitable to mixed finite element formulation, is obtained. Functional is derived by using the variational principles; Gateaux differential and potential operator concept. The mixed finite element is also capable to handle the uniform variation of the thickness. The explicit form of the rectangular element is given. A quadrilateral element can be obtained by using a 2×2 Gauss quadrature. Element has four corner nodes and 36 degrees of freedom. The nodal unknowns are; three displacements, three membrane forces, two bending and a torsional moment. Element is first verified by a well-known static problem present in the literature and later on variable cross-sectional hypars are solved.