Physically based deformation animation is an important topic in computer graphics, which has become a research focus. Thin shell is a special model of deformable models, such as hats, leaves, balloons and so on, which can be found anywhere in our life. As a result, thin shell deformation is widely used in animations, movies and simulation systems. However, thin shell model has different nature from other models. Its thickness is small compared to its other dimensions. This nature is similar to thin plate model. Thin shell model has a curved rest configuration, not a flat one of thin plate model.

Among the deformation methods, finite element method is based on continuum mechanics, which is more accurate and convergent than discrete models like mass spring system. Besides, finite element method can capture volumetric effects such as volume preservation. In recent years, deformation simulations based on finite element method have made great progress, and this is also used in our system.

Different from other thin shells, balloons have special nature: more stretching, less bending and shearing, incompressible. Previously deformation methods often focus on 3d models or thin plate models such as cloth. The rest thin shell methods are complex or ignore the special nature of thin shells especially balloons.

In this paper, a simple thin shell deformation algorithm using finite element method is introduced, which is used to simulate the deformation of balloons inflating animation. Considering the nature of balloons, volume preservation algorithm and gas model are added. The triangle element is modified to simple three-prism element, ignoring bending and shearing, and volume preservation algorithm is used to match the incompressible nature of balloons. During inflating, the movement of gas is very small compared with the stretching of rubber, so the gas model is very simple, ignoring the movement of gas. In this way, the algorithm is very simple with an acceptable accuracy. In the end of this paper, this method is tested on different balloon examples including comparison with other methods.