K. Rajaiah

Hole-shape optimization in a finite plate in the presence of auxiliary holes

Minimizing the stress concentration around holes in uniaxially loaded finite plates is an important consideration in engineering design. One method for reducing the stress concentration around a central circular hole in a uniaxially loaded plate is to introduce smaller auxiliary holes on either side of the original hole to help smooth the flow of the tensile principal-stress trajectories past the original hole. This method has been demonstrated by Heywood and systematically studied by Erickson and Riley. Erickson and Riley show that for a central-hole diameter-to-plate width ratio of 0.222, the maximum stress reduction is up to 16 percent. In recent work, Durelliet al. show that the stress concentrations around holes in uniaxially loaded plates can be minimized by changing the hole shape itself till an optimum hole profile with constant stress values respectively on the tensile and compressive segments of the hole boundary is reached. By this technique the maximum stress reduction obtained for the above case is up to 20 percent.In the present work, starting with the optimum sizes and locations of central and auxiliary circular holes for a finite plate given by Erickson and Riley, a systematic study of the hole-shape optimization is undertaken. A two-dimensional photoelastic method is used. For a central-hole diameter-to-plate width ratio of 0.222, the reduction in stress-concentration factor obtained after hole-shape optimization is about 30 percent. It is also shown that it is possible to introduce the ‘equivalent ellipse’ concept for optimized holes.

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 efficiency

Optimum hole shape determination in infinite orthotropic plates under inplane loading by conformal transformation

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 }^ + }}

Optimum Quasi-Rectangular Holes in Infinite Orthotropic Plates Under Inplane Loading

where

Optimum hole shapes in circular cylindrical shells under tension and torsion

\sigma _{a\ell \ell }

4. ENTREPRENEURSHIP DEVELOPMENT: A STUDY OF MSMEs IN CHITTOOR DISTRICT

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.