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Lighter and stronger

Method to optimize holes and fillets minimizing stress concentrations, decreasing weight and in many cases, increasing strength

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Abstract

A new method has been developed that permits the direct design of shapes of two-dimensional structures, loaded in their plane, within specified design constrains and exhibiting optimum distribution of stresses. The method uses photoelasticity and requires a large-field diffused-light polariscope. The optimization process involves the removal of material (with a hand filer or router) from the low-stress portions of the hole boundary of the model till an isochromatic fringe coincides with the boundary both on the tensile and compressive segments.

The degree of optimization is evaluated by means of coefficient of efficiency

$$K_{eff} = \frac{1}{{s_2 - s_0 }} \frac{{\int_{s_0 }^{s_1 } {\sigma _t^ + } ds}}{{\sigma _{a\ell \ell }^ + }} \frac{{\int_{s_1 }^{s_2 } {\sigma _t^ - } ds}}{{\sigma _{a\ell \ell }^ + }}$$

where\(\sigma _{a\ell \ell } \) represents the maximum allowable stress (the positive and negative superscripts referring to tensile and compressive stresses, respectively),S 0 andS 1 are the limiting points of the segment of boundary subjected to tensile stresses andS 1 andS 2 are the limiting points of the segment of boundary with compressive stresses.

Several problems of optimization related to the presence of holes in finite and infinite plates, subjected to uniaxial and biaxial loadings and in disks subjected to diametral loading, are solved parametrically. Some unexpected results have been found: (1) the optimum shape of a hole in a large plate, subjected to uniaxial load has a stress-concentration factor of 2.5 compared to 3 for the circular hole. The sides parallel to the load have a ‘barrel’ shape; (2) the optimum shape of a large hole in a narrow bar of finite width, subjected to uniaxial load, is ‘quasi’ square, but the transverse boundary has the configuration of a ‘hat’; (3) for the small hole in the large plate, under biaxial loading of equal and opposite sign, a double-barrel shape has a lower stress-concentration factor than the circular hole. In all these cases, there is appreciable saving in material. (4) The optimum, shape of a tube, subjected to diametral compression, has small ‘hinges’ and is much lighter and stronger than the circular tube. Fracture in a brittle material does not start at the hinge. Applications are also shown to the design of dove tails and slots in turbine blades and rotors, and to the design of star-shaped solid propellant grains for rockets, for both the case of parallel side rays and enlarged tip of rays. A parametric solution is given for this last case.

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Authors and Affiliations

  1. School of Engineering, Oakland University, 48063, Rochester, MI

    A. J. Durelli (Professor of Engineering)

  2. Indian Institute of Technology, Powai, 400 076, Bombay, India

    K. Rajaiah (Professor)

Authors
  1. A. J. Durelli
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  2. K. Rajaiah
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Durelli, A.J., Rajaiah, K. Lighter and stronger. Experimental Mechanics 20, 369–380 (1980). https://doi.org/10.1007/BF02321012

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  • DOI: https://doi.org/10.1007/BF02321012

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