Abstract
A scheme of a statically definable truss with additional supports is proposed. Derive formulas for the dependence of the deflection of the truss against the number of panels for three types of symmetrical loads. It is shown that for definite numbers of panels the determinant of the system of equations for the equilibrium of nodes degenerates. This indicates an instant changeability of the structure. To generalize particular solutions to an arbitrary number of panels, the induction method is applied. For this purpose, in the computer mathematics system Maple linear recurrence equations are constructed for the terms of a sequence of coefficients from individual solutions. The graphs of the dependences obtained indicate a nonmonotonic character of the solutions found and the possibility of optimizing the design by choosing the number of panels.
Highlights
A scheme of a statically definable truss with additional supports is proposed
The first trial calculations in symbolic form according to the compiled program showed that the truss has a well hidden fault
This is manifested in the fact that for some values of n the determinant of the system becomes zero
Summary
A scheme of a statically definable truss with additional supports is proposed. Derive formulas for the dependence of the deflection of the truss against the number of panels for three types of symmetrical loads. It is shown that for definite numbers of panels the determinant of the system of equations for the equilibrium of nodes degenerates. This indicates an instant changeability of the structure. To generalize particular solutions to an arbitrary number of panels, the induction method is applied. For this purpose, in the computer mathematics system Maple linear recurrence equations are constructed for the terms of a sequence of coefficients from individual solutions. From the solution of the matrix equation GS B , where S — is the vector of all forces in the rods, B — the load vector, the forces are obtained in the symbolic form. The displacement of the middle node of the lower belt is determined by the Maxwell-Mohr's integral m 5
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