A. J. Durelli

Optimization of geometric discontinuities in stress fields

The ideal boundary of a discontinuity is defined as that boundary along which there is no stress concentration. Photoelastically an isochromatic coincides with the ideal boundary. This property is used to develop experimentally ideal boundaries for some cases of technological interest. The concept of ‘coefficient of efficiency’ is introduced to evaluate the degree of optimization. The procedure to idealize boundaries is illustrated for the two cases of the circular tube and of the perforated rectangular plate, with prescribed functional restraints and a particular criterion for failure. An ideal design of the inside boundary of the tube is developed which decreases its maximum stress by 25 percent, at the time it also decreases its weight by 10 percent. The efficiency coefficient is increased from 0.59 to 0.95. Tests with a brittle material show an increase in strength of 20 percent. An ideal design of the boundary of the hole in the plate reduces the maximum stresses by 26 percent and increases the coefficient of efficiency from 0.54 to 0.90.

Lighter and stronger

AbstractA 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 efficiencyn

Determination of strains in photoelastic coatings

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

Photoelastic analysis of interlaminar matrix stresses in fibrous composite models

n wheren

On the history of some recent measurements described inexperimental mechanics

sigma _{aell ell }

Photoelastic investigation of a shrink-fit problem

n represents the maximum allowable stress (the positive and negative superscripts referring to tensile and compressive stresses, respectively),S0 andS1 are the limiting points of the segment of boundary subjected to tensile stresses andS1 andS2 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.