Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of visco...Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.展开更多
The hypotheses of the Karman-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Th...The hypotheses of the Karman-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Karman equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such ns, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered.展开更多
文摘Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.
基金国家自然科学基金，Development Foundation of Shanghai Municipal Commission of Education，上海市科委资助项目，上海市博士后科研项目
文摘The hypotheses of the Karman-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Karman equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such ns, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered.
