Modeling Of Active Bending By The Method Newton-Raphson And The Modified Newton-Raphson

Abstract

The paper deals with the modelling and analysis of a single layer timber gridshell produced by active bending. Two geometrically nonlinear calculation methods, the Newton-Raphson method and the Modified Newton-Raphson method, are compared for the suitability of active bending modelling. The calculation is presented using the results of the timber lamella bending model. With this analysis, a more stable convergence of the calculation was achieved with the modified Newton-Raphson method than with the Newton-Raphson method. Based on the obtained results, the research was subsequently extended to the bending model of a single-layer network of timber beams, while the applied deformation method was the compression of supports. The suitability of using the modified Newton-Raphson method was verified on the model of a single-layer beam network, and the results were evaluated on five beam network models with different values of initial imperfection. During the processing of the parametric study, two methods of deforming the beam net in its supports were compared. The first method of shaping the beam mesh was the applied load using nodal forces. The second method of shaping the beam network was applied load using nodal displacements.

Keywords

• active bending
• gridshell
• timber
• nonlinearity
• newton-raphson.