The deflection of spatial coatings with periodic structure

Structural mechanics

The scheme of the statically determinate spatial truss is proposed. Rectangular truss has a vertical supports on the sides and loaded uniformly at the nodes by the vertical forces. The forces in the rods and supports are determined using cut nodes method. The dependence of the deflection midspan on a number of panels is obtained. A generalization of the particular solutions on an arbitrary number of panels obtained by the method of induction. All transformations and solutions are made in the system of computer mathematics Maple. The homogeneous linear recurrence equation satisfied by the members of the sequence of coefficients of the desired formula are derived and solved using the special operators of Maple. The formula for deflection is polynomial type in the number of panels. Plots of the deflection of the number of panels, height and the distribution ratio of cross-sectional areas of the rods are given. Expression of forces in the most stretched and compressed rods are obtained to perform durability and structural stability. The found solutions can be used by practical engineers to assess the performance of the designed construction and its optimization.