The article deals with the transition from corrugated plates and shells to smooth structures of equivalent rigidity. An expression for the potential deformation energy of an infinitely small element of an equivalent smooth shell and formulas that establish a connection between internal forces and generalized deformations of a corrugated structure are given. A review of the formulas for the equivalent stiffness of the corrugated shell during bending, presented in the works of various authors, is carried out. In order to select the dependencies that provide the smallest error when replacing the corrugated shell with a smooth one, a numerical experiment is performed in the LIRA finite element complex. A corrugated plate hinged around the contour under the action of a uniformly distributed projective load is considered. The calculation of the structurally orthotropic construction is performed numerically by the finite difference method. It is also established that the monograph of S.G. Lekhnitsky contains an incorrect formula for the moment of inertia of a sinusoidal corrugation.

Keywords: corrugated structures, plates and shells, finite element method, finite difference method, orthotropy, equivalent stiffness

The article discusses the method for calculating beams with corrugated walls as three-layer structures of equivalent rigidity. The derivation of resolving equations for a one-dimensional finite element of a three-layer beam is given. A hypothesis is introduced that the shelves fully perceive normal stresses, and the wall only works on shear. When obtaining the basic equations, forced deformations are taken into account, which may include creep deformations, temperature deformations, shrinkage deformations, etc. The solution of the test problem for a beam hinged at the ends under the action of a load uniformly distributed over the length is presented. To control the reliability of the results, a finite element analysis was performed in a three-dimensional formulation in the LIRA software package. Shelves of the beam are modeled by flat triangular shell finite elements, and the wall is modeled by rectangular shell FE.

Keywords: corrugated wall beam, three-layer beam, finite element method, equivalent rigidity, stress-strain state

The technique of calculating the metal corrugated structures using the finite element method for an axisymmetric load is considered in the article. One-dimensional finite elements in the form of truncated cones are used. Calculations are performed using the program developed by the authors in the Matlab package. An example of calculation of a ground well rigidly clamped in the base under the action of ground pressure is given. The sinusoidal profile of the corrugation is considered. The graphs of changes in bending moments and ring forces are presented. For a smooth shell of the same thickness, the bending moment in the pinch was 30.3% higher compared to the corrugated, and the maximum value of the ring force was 15.7% higher.

Keywords: metal corrugated structures, cylindrical shell, finite element method, axisymmetric problem, soil well, shell theory, edge effect