Author(s)

C. Mattheck, C. Wissner, I. Tesari & K. Bethge

Abstract

The \“Method of Tensile Triangles” was introduced as a design tool that mimics the rules of nature for the shape optimization of a design scheme with respect to increased fatigue life and reduced weight. It 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 may be scaled up and down according to the individual design space limitations of the technical structure. Failure often starts at the cracks tips and slot ends in technical components, because these domains are highly loaded due to stress concentrations. Conventional rounding or drilling away of these crack tips can only lower the stresses. By means of the \“Method of Tensile Triangles”, stress concentrations can be minimized and the endings redesigned and compressed. In this paper the \“Method of Tensile Triangles” will be explained and it will be shown, by results of Finite Element analyses, how the destructive effect of crack tips and slot ends in technical components can be eliminated. Keywords: method of tensile triangles, shape optimization, crack arrest, stress concentrations. 1 Introduction Good mechanical constructions are reliable during their estimated lifetime, are light-weight and have a high load-capability. One of the main reasons for failure is local stress concentrations, which occur where the force flow is disturbed, e.g. at notches even if they are rounded and not sharp. The stress concentrations at notches on the surface of a component cause material fatigue during its lifetime. Therefore, the prevention of such stress-raising effects is of great importance in nature as well as in engineering design. Trees make any effort to grow into a

Keywords

method of tensile triangles, shape optimization, crack arrest, stress concentrations