An Adaptive Geometrically-exact Formulation For Large-scale Membrane Structures

In order to describe the large deformation of the membrane structure in the relaxed state accurately,the balanced state between the bending stress and the stretching stress.In order to describe when the membrane structure is restored to tension state accurately,a new calculation model is established in this paper.(1)An adaptive geometrically-exact membrane theory is established.According to the instantaneous stress of a particle on the membrane structure,the particle is automatically selected to simulate the equilibrium and dynamics of the large-scale membrane structure using a membrane model or a plate/shell model.(2)A high-accuracy triangular element:For membrane model,the amount of calculation is small;For plate/shell model,there are no numerical problems such as shear locking and membrane locking.In the dynamics calculations of large-scale membrane structures,most of the membrane structures are always under tension state at most times,so the bending,warping,and torsion effects of the membrane will be ignored.The membrane theory has been sufficiently precisely described,but the relaxation effect may appear at certain times at some point in the membrane,even wrinkling.In order to precisely describe the large deformation of a membrane in tension state or a wrinkle state,a large deformation plat/shell theory is needed.The amount of calculation of the plate/shell model is significantly larger than that of the membrane model,but the whole response of the membrane structure cann?t be found easily.However,compared with the membrane model,the amount of calculation of plate/shell model is much larger and cause a lot of waste of computing resources.Therefore,it is necessary to develop a new adaptive theory,which can be used to simulate the membrane structure adaptively by membrane model or plate/shell model according to the local tension or relaxation state of the membrane structure at any time at any position.Or,to design a model,the same state parameters can be used to describe membrane and the plate /shell at the same time,only the expressions of elastic potential energy,thegeneralized force and the Jacobi are different.The idea of this paper is to study the equilibrium and dynamics of large membrane structures by using the method of adaptive model.Guided by principles of continuum mechanics,firstly,it is judged whether a particle is in a tension or relaxation state.Then according to the data of the instantaneous stress of the particle in the membrane structure,the particle will be adaptively chosen to accurately reflect the equilibrium and dynamics of the membrane structure with the membrane model or the plate/shell model.In addition,this paper is prepared to establish a new set of high-precision triangular elements to disperse large membrane structures with arbitrary connection conditions,arbitrary shapes and support conditions.In this way,Any relaxation at any position in a triangular element of a membrane structure can be accurately judged.And more importantly,the efficiency of the calculation can be improved continuously,and the shape and dynamics of the relaxation state can still be accurately satisfied.The accuracy of the model in this paper can be tested by the standard example of flexible multibody system and the standard model in the finite element theory.The errors of the adaptive model and the plate/shell model are controlled within 0.50%.The errors of the adaptive model and other reference values are controlled within 5%.