The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the...The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.展开更多
Gas fluidization has an ability to turn static particles to fluid-like dense flow, which allows greatly improved heat transfer among porous powders and highly efficient solid processing to become reality. As the risin...Gas fluidization has an ability to turn static particles to fluid-like dense flow, which allows greatly improved heat transfer among porous powders and highly efficient solid processing to become reality. As the rising star of current scientific research, some nanoparticles can also be fluidized in the form of agglomerates, with sizes ranging from tens to hundreds of microns. Herein, we have reviewed the recent progress on nanomaterial agglomeration and their fluidization behavior, the assisted techniques to enhance the fluidization of nanomaterials,including some mechanical measures, external fields and improved gas injections, as well as their effects on solid fluidization and mixing behaviors. Most of these techniques are effective in breaking large agglomerates and promoting particulate fluidization, meanwhile, the solid mixing is intensified under assisted fluidization. The applications of nanofluidization in nanostructured material production and sustainable chemical industry are further presented. In summary, the fluidization science of multidimensional, multicomponent and multifunctional particles, their multi-phase characterization, and the guideline of fluidized bed coupled process are prerequisites for the sustainable development of fluidized bed based materials, energy and chemical industry.展开更多
文摘The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.
基金Supported by the National Natural Science Foundation of China(21306102 and21422604)China Postdoctoral Science Foundation(2015M571049)
文摘Gas fluidization has an ability to turn static particles to fluid-like dense flow, which allows greatly improved heat transfer among porous powders and highly efficient solid processing to become reality. As the rising star of current scientific research, some nanoparticles can also be fluidized in the form of agglomerates, with sizes ranging from tens to hundreds of microns. Herein, we have reviewed the recent progress on nanomaterial agglomeration and their fluidization behavior, the assisted techniques to enhance the fluidization of nanomaterials,including some mechanical measures, external fields and improved gas injections, as well as their effects on solid fluidization and mixing behaviors. Most of these techniques are effective in breaking large agglomerates and promoting particulate fluidization, meanwhile, the solid mixing is intensified under assisted fluidization. The applications of nanofluidization in nanostructured material production and sustainable chemical industry are further presented. In summary, the fluidization science of multidimensional, multicomponent and multifunctional particles, their multi-phase characterization, and the guideline of fluidized bed coupled process are prerequisites for the sustainable development of fluidized bed based materials, energy and chemical industry.
