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285 results on '"Kienzler, Reinhold"'

11. Modularity of the displacement coefficients and complete plate theories in the framework of the consistent-approximation approach

Author

Meyer-Coors, Michael, Kienzler, Reinhold, Schneider, Patrick, Meyer-Coors, Michael, Kienzler, Reinhold, and Schneider, Patrick

Abstract

Starting from the three-dimensional theory of linear elasticity, we arrive at the exact plate problem by the use of Taylor series expansions. Applying the consistent-approximation approach to this problem leads to hierarchic generic plate theories. Mathematically, these plate theories are systems of partial-differential equations (PDEs), which contain the coefficients of the series expansions of the displacements (displacement coefficients) as variables. With the pseudo-reduction method, the PDE systems can be reduced to one main PDE, which is entirely written in the main variable, and several reduction PDEs, each written in the main variable and several non-main variables. So, after solving the main PDE, the reduction PDEs can be solved by insertion of the main variable. As a great disadvantage of the generic plate theories, there are fewer reduction PDEs than non-main variables so that not all of the latter can be determined independently. Within this paper, a modular structure of the displacement coefficients is found and proved. Based on it, we define so-called complete plate theories which enable us to determine all non-main variables independently. Also, a scheme to assemble Nth-order complete plate theories with equations from the generic plate theories is found. As it turns out, the governing PDEs from the complete plate theories fulfill the local boundary conditions and the local form of the equilibrium equations a priori. Furthermore, these results are compared with those of the classical theories and recently published papers on the consistent-approximation approach.

Published
2024

12. A Beam—Just a Beam in Linear Plane Bending

Author

Kienzler, Reinhold, Schneider, Patrick, Öchsner, Andreas, Series Editor, da Silva, Lucas F. M., Series Editor, Altenbach, Holm, Series Editor, Chróścielewski, Jacek, editor, Eremeyev, Victor A., editor, and Wiśniewski, Krzysztof, editor

Published
2019
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28. Dimensioning of thick-walled spherical and cylindrical pressure vessels

Author

Schneider, Patrick, Kienzler, Reinhold, Schneider, Patrick, and Kienzler, Reinhold

Abstract

In this contribution, we revisit the rather classical problem of Lamé and provide a novel and easy way to plot the stress distributions and the overall absolute maximum von Mises stress for arbitrary parameters in only two diagrams. We also provide a maximum hoop stress formula for combined loading and an extensive discussion covering the accuracy of dimensioning via the maximum hoop stress instead of the maximum von Mises stress, as well as the accuracy of the classical approximative hoop stress formulas.

Published
2023

41. Introduction

Author

Kienzler, Reinhold, Herrmann, George, Kienzler, Reinhold, and Herrmann, George

Published
2000
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