The elastic spring behavior of a rhombus frame constructed from non-prismatic beams under large deflection

The spring behavior due to large deflection of a flexible rhombus frame with rigid joints is studied in this paper. The system consists of two equal and opposite diagonal forces that act on two opposite corners of a rhombus frame with a given apex angle γ. The frame sides have a rectangular cross-section and are non-prismatic due to tapering in the section's dimensions. The relations between the large displacement at the corners and the applied forces are obtained using a new robust numerical technique. The technique is based on representing the angular deflection of the side beam by a polynomial on the position variable along the deflected beam axis. The polynomial coefficients are obtained through a numerical optimization procedure based on minimizing the residual error and satisfying the boundary conditions. A classical numerical integration technique is used to verify some of the results obtained by the proposed technique. The frame spring behavior is investigated for different taper ratios and apex angles. The results are transformed into regression relations to utilize its implementation in design and analysis.