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Comparing shapes for stress homogenization in nature and technique
Iwiza Tesari
Last modified: 2009-06-26
Abstract
I. Tesari, C. Mattheck
Forschungszentrum Karlsruhe GmbH
Institute for Materials Research II
Hermann-von-Helmholtz-Platz 1
D-76344 Eggenstein-Leopoldshafen
Germany
Merciless selection pressure of evolution forces biological carrier structures, e.g. trees or bones, to use their material efficiently. For lifetime, they try to achieve as homogeneous a stress distribution as possible and, thus, prevent weak points as well as excessive material consumption. Design principles of natural constructions were studied at the Forschungszentrum Karlsruhe. From them, based on the Finite Element Method (FEM), computer methods were derived for the optimization of technical components. The CAO (Computer Aided Optimization) method simulates adaptive growth. It removes excessive stresses by computer-simulated local material deposition and, thus, homogenizes the stresses on the component surface. In the computer, components grow like trees. Due to the stress reduction the service life of the optimized component is increased compared to the initial value.
A breakthrough towards simplicity was the development of the simple, purely graphical "Method of Tensile Triangles" (MTT) by Mattheck for the reduction of stress concentrations by notch shape optimization. The Method was inspired by the shape of buttress roots in trees. Like them it bridges a corner-like notch with tensile loaded triangles. The notch shape found with the MTT may be scaled up and down according to the individual design space limitations of the technical structure.
In this paper the Method of Tensile Triangles will be explained and the results of Finite Element Analyses on tension loaded stepped flat bars with circular and by MTT formed notches will be presented. The study shows the effect of this notch shapes on stress concentration factor due to variation of diameter ratio and design space. It also quantifies the amount of design space and mechanical stress which could be lowered by the use of biologic based MTT transitions compared to the "technical" circular rounding.
Forschungszentrum Karlsruhe GmbH
Institute for Materials Research II
Hermann-von-Helmholtz-Platz 1
D-76344 Eggenstein-Leopoldshafen
Germany
Merciless selection pressure of evolution forces biological carrier structures, e.g. trees or bones, to use their material efficiently. For lifetime, they try to achieve as homogeneous a stress distribution as possible and, thus, prevent weak points as well as excessive material consumption. Design principles of natural constructions were studied at the Forschungszentrum Karlsruhe. From them, based on the Finite Element Method (FEM), computer methods were derived for the optimization of technical components. The CAO (Computer Aided Optimization) method simulates adaptive growth. It removes excessive stresses by computer-simulated local material deposition and, thus, homogenizes the stresses on the component surface. In the computer, components grow like trees. Due to the stress reduction the service life of the optimized component is increased compared to the initial value.
A breakthrough towards simplicity was the development of the simple, purely graphical "Method of Tensile Triangles" (MTT) by Mattheck for the reduction of stress concentrations by notch shape optimization. The Method was inspired by the shape of buttress roots in trees. Like them it bridges a corner-like notch with tensile loaded triangles. The notch shape found with the MTT may be scaled up and down according to the individual design space limitations of the technical structure.
In this paper the Method of Tensile Triangles will be explained and the results of Finite Element Analyses on tension loaded stepped flat bars with circular and by MTT formed notches will be presented. The study shows the effect of this notch shapes on stress concentration factor due to variation of diameter ratio and design space. It also quantifies the amount of design space and mechanical stress which could be lowered by the use of biologic based MTT transitions compared to the "technical" circular rounding.