不静定立体トラス平板の差分法による解法(その1)

Abstract

In the previous report, an analysis has been made to the gridworks by the application of difference equation. This time it is intented to analyze the statically indeterminate space trussed flat plate by difference method. In discussing the solution of plate, it is of adventage to find out the equations of deformation in the form of series from the equations of equilibrium and the method of elastic weights regarding plane warren-type trusses. By transforming the corresponding equations, we may obtain difference equations which show the relations between the deformations and loads. Then, in discussing the problem in contrast with gridworks which have been referred to in the previous report, the relations between deformation and load of grid truss are derived in difference forms. Now before we go into any further, let us explain the character of the space trussed flat plate, the upper and the lower chords of which meet at right angles one another at regular intervals in plane projection and by tying up the points of these intersections diagonally with lattice members, it would form space trussed flat plate mentioned. For the solution of the problem, we first choose the stress of each chord on these space trusses of isotropy as unknown quantities, and eliminate the stress of lattice members which are derived from the conditions of equibrium at each point, and obtain force equilibrium in form of difference equations, by which the relations between the stress of chords chosen and arbitrary loads at each points are shown. These equations can be also obtained by modifying coefficients referred to in the previous report of the statically determinate space truss shell in such manner as may be applicable to plate.