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The trapezoidal finite element in absolute coordinates for dynamic modeling of automotive tire and air spring bellows. Part 1: equations of motion

Pogorelov Dmitry, Rodikov Alexander

Transport Problems

2021

T. 16, z. 2

141--152

Equations of motion of a finite element in absolute coordinates including mass matrix, generalized inertia and internal forces are derived. A trapezoidal element for dynamic models of flexible shells in the shape of surface of revolution is considered. The element can be used for modeling dynamics of automotive tire and air spring bellows and some other flexible elements of transport systems undergoing large elastic deflections.

The trapezoidal finite element in absolute coordinates for dynamic modeling of automotive tire and air spring bellows. Part II: verification

Pogorelov Dmitry, Rodikov Alexander

Transport Problems

2021

T. 16, z. 3

5--16

The second part of the paper includes numerical tests verifying equations of motion of flexible bodies in absolute coordinates with rectangle and isosceles trapezoid finite elements. The equations are formulated in the first part of the paper. The verification is based on three types of problems: calculation of natural frequencies and modes, evaluation of buckling, and computation of large static and dynamic deflections of flexible bodies. Tests show good agreement with the theoretical results and the results obtained by other authors.