Obliczanie Powierzchni Wpływowych dla Płyt Równoległobocznych - Suchar, M. (Engineering Transactions, 1959)
This paper is devoted to the computation of influence surfaces (Green's functions) for plates having the form of parallelograms. An oblique rectilinear system is considered the axes of which are parallel to the sides of the plate. The assumptions are those of the classical theory of thin plates with small deflections, and that the plate is homogeneous, anisotropic, perfectly elastic and has at every point one plane of elastic symmetry parallel to the middle plane.In Sec. 1, the relations between the deflection and the cross-section quantities are derived as well as the differential equation of the deflection surface in the case of anisotropy and orthotropy. The boundary conditions are formulated in the simplest cases of support.Sec. 2 contains the computation of the singular parts of the influence surface of deflection for anisotropic, orthotropic and isotropic plates in a manner given by J. Mossakowski for orthogonal coordinates. In Sec. 3 a system of polynomials is given bv means of which regular parts of the influence surfaces may be determined.Finally, a numerical example is considered. This concerns an orthotropic plate in the form of a parallelogram, the sides of which are a = b = 2, the acute angle between the sides being 45°. Two opposite sides are simply supported, the remaining edges are free. The boundary conditions are satisfied in an approximate manner by means of the method of least squares. In order to appraise the convergence of the method used, the three successive approximations for n = 8, 9, 10 are compared by computing the mean errors. Diagrams of contour lines of the influence surfaces for the bending moment, the twisting moment and the shearing force are presented.