Accounting for Displacement of the Shells of Revolution as a Solid in FEM Algorithm.

An algorithm for obtaining the stiffness matrix of a quadrangular finite element of a shell of revolution in the form of a curvilinear fragment of its middle surface has been developed in a curvilinear coordinate system. As the nodal unknowns, we set the components of the displacement vectors of the nodal points and the components of the derivatives of the displacement vectors of the nodes of the finite element. When obtaining approximating functions for the desired values, the form functions of the class C⁽¹⁾ are used for the vector value of the internal point of the finite element that is expressed via the vector values of the nodal points. After coordinate transformations of form functions of class C⁽¹⁾ based on the parameters of the used curvilinear coordinate system, the necessary approximating expressions for the desired quantities, the use of which leads to taking into account the displacement of the finite element as a solid, are obtained. An algorithm for assigning boundary conditions for the accepted nodal unknowns is presented. The possibility of realizing the conditions for conjugation of shells of revolution using the developed finite element is shown. Specific test examples show the high efficiency of the proposed approximation method with allowance for displacement of the shell as a solid under the action of a given load. [ABSTRACT FROM AUTHOR]