Research On Approximation And Optimization Of Generalized Cylindrical Target Surfaces Based On Waterbomb Origami

Origami technology shows its potential to approximate three-dimensional surfaces by designing crease patterns on flat materials and folding three-dimensional structures along the creases.With the rapid development of computer-aided geometric design and computer-aided design technology,simple two-dimensional materials are transformed into complex threedimensional structures,which are widely used in engineering and other fields,arousing the interest of scientists and engineers in their characteristic research.The design of the threedimensional structure of origami begins with the design of origami patterns,also known as basic patterns,which consist of either replicated or similar elements.Waterbomb origami structure is one of the most widely studied modes in contemporary engineering.However,due to the potential geometric constraints limiting the design space,users cannot easily use this kind of origami to fit the target surface.Based on the above issues,this thesis proposes a waterbomb origami approximation method for generalized cylindrical target surfaces is proposed,the main research work is as follows:Firstly,an inverse design method for approximate generalized cylindrical target surfaces based on six-fold waterbomb origami is proposed.Considering symmetry and periodic repeatability,a single strip of waterbomb origami was first modeled and then longitudinally replicated to generate a generalized cylindrical waterbomb origami structure.In order to achieve flat-foldability,an iterative optimization procedure is introduced to minimize flatfoldability residuals.A precision method is developed to obtain the normalized crease pattern and adjust the two-dimensional pattern.Based on this,the thesis also demonstrates a waterbomb-derived origami based rectangular fill structure to amplify the design variation.In addition,rigid folding sequences and several physical engineering structures are introduced.Based on the above research methods,improvements and perfection have been made in terms of the diversity and effectiveness of origami.On the other hand,considering the possibility of physical self-intersection and other phenomena in the flat state of the six-fold waterbomb origami unit,this thesis proposes a shape design method based on the approximate generalized cylindrical target surfaces of the seven-fold waterbomb origami unit,which splits the middle vertices of the six-fold waterbomb origami unit,which can effectively avoid the above phenomena.Due to symmetry and periodic replication,it also starts with constructing a six-fold waterbomb origami strip and introducing optimization algorithms to minimize scalability and flatness errors.To reduce the degree of freedom of the origami structure,a derived structure was constructed based on it.Finally,this thesis also simulated the rigid folding motion of the origami structure.The methods proposed above can be used to facilitate the design of origami-inspired structures for various engineering purposes,such as foldable shelters,tubular structures,metamaterials,etc.In future work,it would be meaningful to explore the possibility of approximating the shape of different curved objects by continuous folding motion based on the same waterbomb origami.Such exploration can be used to stimulate the application of new self-deformable structures in specific scenarios.