TY - JOUR
T1 - Natural shape functions of a compressed Vlasov element
AU - Leung, A. Y T
PY - 1991
Y1 - 1991
N2 - To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly. © 1991.
AB - To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly. © 1991.
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U2 - 10.1016/0263-8231(91)90037-J
DO - 10.1016/0263-8231(91)90037-J
M3 - RGC 21 - Publication in refereed journal
VL - 11
SP - 431
EP - 438
JO - Thin-Walled Structures
JF - Thin-Walled Structures
SN - 0263-8231
IS - 5
ER -