不静定立体トラス平板の差分法による解法(その2)

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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 from 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 chraactor 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 from 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. Then, the equations of deformtions are introduced by applying the method of elastic weights horizontally at each point and the relations between each chord are expressed in form of difference equation. By transformations of the former equations and force equilibrium referred to in the preceding paragraph, the relations between stress of each chord and arditrary loads in upper chords are derived in difference forms. In addition to the exact solution we abtained by the methods already mentioned, an approximate method is devised neglecting shearing deformation. Also the relations between deflection and stress of each chord are derived in form of difference equations through the application of three dimensional method used in plane warren-type truss. Using some examples, difference equations so obtained are analyzed with respect to various boundary conditions by the solution of linear equations. As the results of analysis, the values obtained by the exact solution and the approximate method are compared, and the approximate method so devised was proved to de useful. The differences of gridworks and space trussess are easily comparable by the values of axis forces in the plane of space trusses. Some of the equations of deformtion and load among a group of difference equations have similar from, and the difference equations of gridworks and space trusses are compared with the differential equations of plate. Until quite recently, it has been believed to be a puzzling problem to solve the space trussed plate of the statically indeterminate structure of high order, but by the analysis and calculations of the difference equations so derived by the method already mentioned, the values of stress and deformation can be readily obtained in solving plate problem.
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不静定立体トラス平板の差分法による解法(その2)

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