Reshaping of tensegrities using a geometrical variation approach

• We propose a novel iterative approach for the reshaping of tensegrities.
• Reshaping is performed using a geometrical variation approach.
• An underdetermined linearized form of nonlinear equilibrium equations is used.
• The method generates very accurate results with a remarkable convergence rate.

We propose a novel approach for the reshaping of tensegrities and pre-stressed pin-jointed frameworks. Both free standing and restrained frameworks are studied. First, a geometrical variation is introduced and considered as an initial geometrical change to a self-equilibrated tensegrity. A new nonlinear set of equilibrium equations is then established based on this variation and subsequently linearized using an expansion. The linearization provides us with an underdetermined system of linear equations with a rectangular Jacobian matrix which is derived in a very simple and compact matrix form. The system is finally solved iteratively using a Newton–Raphson method employing a Moore–Penrose pseudo inverse operation to establish a new equilibrium state. The method promises to generate very accurate results with a remarkable convergence rate. The outstanding features and performance of the proposed method are demonstrated and studied comprehensively through three examples.