Volumetric discretization element with invariant displacements approximation in the SSS numerical analysis problems for the building structures

The article describes the sought quantities invariant approximation method in relation to the volumetric discretization element in the form of a parallelepiped with the main nodes located at its vertices. The displacement vector components and their partial derivatives of the first order were selected as the sought-for unknowns of the volume discretization element. An approximating expression when implementing the invariant approximation technique is written for the displacement vector of an element inner zone point and not for components of this vector isolated from each other. The approximating expressions obtained on the sought quantities’ invariant approximation basis contain the curvilinear coordinates system parameters used. The discretization volume element compatibility is improved due to the use of Lagrange multipliers in additional nodes located in the middle of the parallelepiped bases’ edges. The Lagrange correction factors ensure the displacement vectors normal components derivatives’ equality along the normals to the element base edges’ midpoints. The expanded stiffness matrix and the column of the volumetric discretization element nodal forces are formed by minimizing the conditional Lagrange functional.