Under certain conditions, the dynamic equations of membrane shells and the dynamic equations of flexural shells are obtained from dynamic equations of Koiter shells by the method of asymptotic analysis.
In this paper, we consider the linearly viscoelastic equations for Koiter shells. Also, we prove the existence and uniqueness of the solution by Galerkin method.
We define two nonlinear shell models whereby the deformation of an elastic shell with small thickness minimizes ad hoc functionals over sets of admissible deformations of Kirchhoff-Love type. We establish that both mo...We define two nonlinear shell models whereby the deformation of an elastic shell with small thickness minimizes ad hoc functionals over sets of admissible deformations of Kirchhoff-Love type. We establish that both models are close in a specific sense to the well-known nonlinear shell model of W.T. Koiter and that one of them has a solution, by contrast with Koiter's model for which such an existence theorem is yet to be proven.展开更多
By applying the inequality of Korn＇s type without boundary conditions on a general surface, we prove that the scaled displacement of the two-dimensional linearly viscoelastic Koiter＇s shell converges to the solution...By applying the inequality of Korn＇s type without boundary conditions on a general surface, we prove that the scaled displacement of the two-dimensional linearly viscoelastic Koiter＇s shell converges to the solution of two-dimensional model system of linearly viscoelastic ＂membrane＂ shell.展开更多
在结构屈曲分析理论研究的历史中,柯以特(K o iter)理论是一个里程碑.他对屈曲分析理论的观点至今仍然被视为经典.因此,格外有必要了解柯以特理论的构成及其在结构屈曲分析中的指导作用,同时也有必要了解柯以特理论的局限性.本文所介绍...在结构屈曲分析理论研究的历史中,柯以特(K o iter)理论是一个里程碑.他对屈曲分析理论的观点至今仍然被视为经典.因此,格外有必要了解柯以特理论的构成及其在结构屈曲分析中的指导作用,同时也有必要了解柯以特理论的局限性.本文所介绍、论述的柯以特理论是屈曲分析理论的研究基础.展开更多
The human tricuspid valve, one of the key cardiac structures, plays an important role in the circulatory system. However, there are few mathematical models to accurately simulate it.In this paper, firstly, we consider...The human tricuspid valve, one of the key cardiac structures, plays an important role in the circulatory system. However, there are few mathematical models to accurately simulate it.In this paper, firstly, we consider the tricuspid valve as an elastic shell with a specific shape and establish its novel geometric model. Concretely, the anterior, the posterior and the septal leaflets of the valve are supposed to be portions of the union of two interfacing semi-elliptic cylindrical shells when they are fully open.Next, we use Koiter's linear shell model to describe the tricuspid valve leaflets in the static case, and provide a numerical scheme for this elastostatics model. Specifically, we discretize the space variable, i.e., the two tangent components of the displacement are discretized by using conforming finite elements(linear triangles) and the normal component of the displacement is discretized by using conforming Hsieh-Clough-Tocher triangles(HCT triangles).Finally, we make numerical experiments for the tricuspid valve and analyze the outcome. The numerical results show that the proposed mathematical model describes well the human tricuspid valve subjected to applied forces.展开更多
To solve the shell problem, we propose a mixed finite element method with bubble-stabili -zation term and discrete Riesz-representation operators. It is shown that this new method is coercive, implytng the well-known ...To solve the shell problem, we propose a mixed finite element method with bubble-stabili -zation term and discrete Riesz-representation operators. It is shown that this new method is coercive, implytng the well-known X-ellipticity and the Inf-Sup condition being circumvented, and the resulting linear system is symmetrically positively definite, with a condition number being at most O(h-2). Further, an optimal error bound is attained.展开更多
Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface w...Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface without boundary. The idea is to use a finite number of maps fordefining the surface and the inequality of Korn's type without boundary conditions for everymap and to recast these in a general functional analysis setting about quotient spaces.展开更多
文摘In this paper, the dynamic equations for Koiter shells have been studied by Galerkin method, the existence and uniqueness to the solutions are proved.
基金the National Natural Science Foundation of China (No.10071024).
文摘Under certain conditions, the dynamic equations of membrane shells and the dynamic equations of flexural shells are obtained from dynamic equations of Koiter shells by the method of asymptotic analysis.
基金Supported by National Natural Science Foundation of China (No.10271030)Foundation of Qufu Normal University for Ph.D.
文摘In this paper, we consider the linearly viscoelastic equations for Koiter shells. Also, we prove the existence and uniqueness of the solution by Galerkin method.
文摘We define two nonlinear shell models whereby the deformation of an elastic shell with small thickness minimizes ad hoc functionals over sets of admissible deformations of Kirchhoff-Love type. We establish that both models are close in a specific sense to the well-known nonlinear shell model of W.T. Koiter and that one of them has a solution, by contrast with Koiter's model for which such an existence theorem is yet to be proven.
基金National Natural Science Foundation of China(No.10271030)Foundation of Qufu Normal University for Ph.D
文摘By applying the inequality of Korn＇s type without boundary conditions on a general surface, we prove that the scaled displacement of the two-dimensional linearly viscoelastic Koiter＇s shell converges to the solution of two-dimensional model system of linearly viscoelastic ＂membrane＂ shell.
基金supported by the National Natural Science Foundation of China(Nos.11571275,11572244,11471261,11871399)by the Natural Science Foundation of Shaanxi Province(Nos.2018JM1014,2017JM1005)
文摘The human tricuspid valve, one of the key cardiac structures, plays an important role in the circulatory system. However, there are few mathematical models to accurately simulate it.In this paper, firstly, we consider the tricuspid valve as an elastic shell with a specific shape and establish its novel geometric model. Concretely, the anterior, the posterior and the septal leaflets of the valve are supposed to be portions of the union of two interfacing semi-elliptic cylindrical shells when they are fully open.Next, we use Koiter's linear shell model to describe the tricuspid valve leaflets in the static case, and provide a numerical scheme for this elastostatics model. Specifically, we discretize the space variable, i.e., the two tangent components of the displacement are discretized by using conforming finite elements(linear triangles) and the normal component of the displacement is discretized by using conforming Hsieh-Clough-Tocher triangles(HCT triangles).Finally, we make numerical experiments for the tricuspid valve and analyze the outcome. The numerical results show that the proposed mathematical model describes well the human tricuspid valve subjected to applied forces.
基金China University of Geo-sciences and the Natural Sciences Foundation of HeiLong Jiang Province.
文摘To solve the shell problem, we propose a mixed finite element method with bubble-stabili -zation term and discrete Riesz-representation operators. It is shown that this new method is coercive, implytng the well-known X-ellipticity and the Inf-Sup condition being circumvented, and the resulting linear system is symmetrically positively definite, with a condition number being at most O(h-2). Further, an optimal error bound is attained.
文摘Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface without boundary. The idea is to use a finite number of maps fordefining the surface and the inequality of Korn's type without boundary conditions for everymap and to recast these in a general functional analysis setting about quotient spaces.
