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The paper describes the application of boundary-point-least-squares method (BPLS) for the determination of stresses in multiply connected finite orthotropic plates under plane stress. Series solutions composed of mapping functions are employed. Numerical solutions presented include the case of an orthotropic plate with an elliptical hole with orientation noncoincident with the material axes.

The effect of a free edge on the stress distribution in several uni directional composite plates is presented. Plates with one, two, and three rows of equally spaced fibers are considered. The fibers and matrix are elastic and isotropic. Two types of loading conditions are investigated. The first is a uniform extension transverse to the fiber direction. The second is a linearly varying "bending" displacement transverse to the fiber direction. Stress and displacement solutions are obtained by the boundary point least squares method. For both loading conditions considered, the results show that the effect of the free edge extends only to the outer fiber nearest the free edge and the stress distribution in and around the remaining "inside" fibers is essentially equivalent to stresses for a fiber embedded in a doubly periodic array. For the case of uniform extension, effective transverse moduli are computed for the one, two, and three fiber plates and compared with the effective transverse modulus for an infinite plate.

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

This paper concerns the numerical solution of shallow spherical shell problems by the method of boundary-point-least-squares. The analysis forms the basis of a computer program for the calculation of stresses in curved perforated plates. Multiple-pole series solutions are used, and recursion methods for generating the required Bessel-Kelvin functions are discussed. Numerical results are given for previously unsolved problems involving an array of seven circular holes and for an array of four noncircular holes.