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    <subfield code="a">Liu, Chen-liang</subfield>
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    <subfield code="a">Development of a cylindrical element for pipe analysis</subfield>
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    <subfield code="a">A general formulation of a family of ''macro pipe elanents" is  presented for a more efficient and rigorous analysis of piping systems subjected to static loadings. The degeneration concept is utilized in the development of this element family. Displacement fields and the geometry of these elements are described in terms of their respective nodal values by the shape functions product of a Lagrangian polynomial in the longitudinal direction and a truncated Fourier series in the  circumferential direction. To avoid "shear locking" in the extremely thin pipe situation, a reduced integration scheme is employed for the transverse shear energy. Several examples are tested to investigate the  general performance of this element family and satisfactory results are obtained. </subfield>
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