A two-node curved axisymmetric shell element based on coupled displacement field

An e$cient two-node curved axisymmetric shell element is proposed. The element with three degrees of freedom per node accounts for the transverse shear #exibility and rotary inertia. The strain components are de"ned in a curvilinear co-ordinate frame. The variation of normal displacement (w) along the meridian is represented by a cubic polynomial. The relevant constitutive relations and the di!erential equations of equilibrium in the meridional plane of the shell are used to derive the polynomial "eld for the tangential displacement (u) and section rotation (h). This results in interdependent polynomials for the "eld variables w, u and h, whose coe$cients are coupled by generalized degrees of freedom and geometric and material properties of the element. These coupled polynomials lead to consistently vanishing coe$cients for the membrane and transverse shear strain "elds even in the limit of extreme thinness, without producing any spurious constraints. Thus the element is devoid of membrane and shear locking in thin limit of inextensible and shearless bending, respectively. Full Gaussian integration rules are employed for evaluating sti!ness marix, consistent load vector and consistent mass matrix. Numerical results are presented for axisymmetric deep/shallow shells having curved/straight meridional geometries for static and free vibration analyses. The accuracy and convergence characteristics of this C0 element are superior to other elements of the same class. The performance of the element demonstrates its applicability over a wide range of axisymmetric shell con"gurations.