Research On Computational Theory And Applications Of Finite Particle Method For Membrane Structures

The membrane structure is a typical flexible tensioned system. Unlike the structures made of rigid members, the bending and shear resistance of membrane material is almost negligible and consequently prestress is absolutely basic to the structural stiffness. And thus nonlinearities are their distinguishing features. Given the advantage of the finite particle method (FPM) in the analysis of complicated nonlinear behavior, in this dissertation the computational theory of the FPM for membrane structures has been further developed on the basis of previous researches. Moreover, it has been served as a fundamental analysis tool for an intensive research and investigation towards some general or difficult issues and critical technique challenges on the study of membrane structures.This dissertation has described the research status quo of the typical theoretical and numerical methods for the analysis of membrane structures and their applications in engineering. The essential mechanical characteristics and some issues of concerned are presented. Taken into account the advantage of the FPM, the main research work of this dissertation is briefly introduced.Different from the traditional methods derived from continuum mechanics and variational principle, the FPM is rooted in vector mechanics. With the concept of’point value description’,’path unit’and’fictitious motion’, the FPM models the analyzed domain in a physical form instead of a mathematical form. Structural geometric nonlinearity and dynamic behavior can be naturally handled by this method. These features make the FPM have advantages in dealing with the complicated behaviors of structures, such as large deflection, material nonlinearity, coupling of rigid-body and deformations, discontinuities, etc. This work systematically expounds the fundamentals of the FPM and derives the formulations of3D membrane in detail, with a special treatment for the particles containing motion restrictions. In general, the basic numerical analysis tools of this dissertation are established.The initial shape analysis method with the FPM at the core is developed. For the two kinds of membrane structures prestressed in different ways, i.e. tensioned membrane structures and inflatable membrane structures, corresponding analysis ideas and algorithm procedures of shape analysis are presented respectively. To achieve the equilibrium shape as fast as possible, an integral-form time integration scheme has been proposed for solving the equation of motion. Besides, some crucial strategies for solving the minimal surfaces or non-isotropic stress surface and controlling particle distributions to avoid distortions are given and discussed, which are successfully applied in the shape analysis of pure membrane structures. Two novel ideas for the shape analysis of cable-strut-membrane structures are presented, namely assuming fictitious internal forces of cables/bars and restricting positions of cables/bars. For the inflatable membranes controlled by the inner pressure and height or volume, a two phase shape analysis algorithm with form finding and force finding one after another is developed.A large deformation numerical algorithm considering the anisotropy and nonlinearity of the membrane material in loading analysis is presented. Based on the actual mechanical properties of membranes, two material models (i.e. orthotropic linear elastic model and anisotropic nonlinear model) implemented in the program are developed. Specially, how to conveniently determine the material principal direction is discussed and a feasible nonlinear model based on the concept of equivalent uniaxial tension is proposed. Nonlinear loading analysis of membrane structures is achieved by the proposed algorithm with the consideration of geometric and material nonlinearity simultaneously.Based on tension-field model, a wrinkling algorithm is developed, and then it is applied to the analysis the effect of structural wrinkling in combination with the nonlinear membrane model. Firstly, according to the state analysis of membranes, we adopt the principal stress-strain combined criterion for judging the wrinkle state. Then, a wrinkling treatment technique based on Raddeman’s model is presented, the basic concept of which is similar to that of the plastic modification technique. Finally, the implementation procedure of the algorithm in the program is presented in detail. There is no restriction for the material models in the proposed algorithm, and that means it is applicable for both linear and nonlinear or isotropic and anisotropic membrane material.In order to achieve the wrinkle details, such as the wavelengths, amplitudes, the number of wrinkles, the accurate wrinkling simulation method is developed based on the shell-bulking theory. Firstly, given the importance of the no-zero bending stiffness of true membranes for acquiring the details of wrinkles and the analogy between wrinkling and bulking, a geometrically nonlinear shell model accounting for both membrane and flexure deformations is specially proposed. Then, several critical techniques are introduced into the wrinkling simulation algorithm. With the remarkable performance of the proposed shell model in tracking nonlinear behaviors, the precise shape of wrinkles in several typical membrane structures and their quantitative evaluations are correctly predicted.Finally, the numerical simulations of complex dynamic behaviors of membrane structures are investigated, including collision-contact, deployment and tearing. From the physical point of view, various models to describe these behaviors are developed, such as the ’point-face’model for collision-contact problems, the multi-gas-chamber flow field model for deployment problems and particle splitting models for tearing problems. Corresponding algorithm procedures in the FPM are presented. With comprehensively applying the theory and algorithm aforementioned developed in this dissertation, the whole processes of various complex dynamic behaviors are simulated, which reveals the availability of the FPM on such issues.Numerical examples demonstrate that the computational theory presented is correct, and the algorithm is effective. Meanwhile, it also promote the FPM into the complex behaviors of membrane structures and provide a new effective analysis tool for engineers and researchers engaged in these studies. The conclusions and problems that should be studied further are summarized at the end of dissertation.