FINITE ELEMENT METHOD ON NUMERICAL SIMULATION OF STRATUM CORNEUM''''S PENETRATION PROPERTY

How the outer substance could penetrate through the skin lies in the stratum corneum, because it is the main barrier in the multi-layers of the skin. Supposing the keratin cell with a special geometry as tetrakaidecahedron, the penetration property of stratum corneum was the key problem which was numerically simulated with finite element method. At first the discretization of the stratum corneum region was given in two steps: first, the discretization of the keratin cell; second, the discretization of fattiness that surrounds the keratin. Then there was the work of numerical simulation. In this procedure, the finite element method and the multi-grid method were used. The former was to obtain the discretization of basic elements; the latter was to decrease the high frequency error. At last the visualization of the numerical simulation was shown.     

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF HETEROGENEOUS MATERIALS WITH VORONOI FINITE ELEMENT METHOD

The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.     

Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method简

An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.     

Finite volume element method for analysis of unsteady reaction–diffusion problems

A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers.     

Improvement of FEM’s dynamic property

The discretization size is limited by the sampling theorem, and the limit is one half of the wavelength of the highest frequency of the problem. However, one half of the wavelength is an ideal value. In general, the discretization size that can ensure the accuracy of the simulation is much smaller than this value in the traditional finite element method. The possible reason of this phenomenon is analyzed in this paper, and an efficient method is given to improve the simulation accuracy.     

MoM-based topology optimization method for planar metallic antenna design

The metallic antenna design problem can be treated as a problem to find the optimal distribution of con-ductive material in a certain domain. Although this problem is well suited for topology optimization method, the volu-metric distribution of conductive material based on 3D finite element method (FEM) has been known to cause numerical bottlenecks such as the skin depth issue, meshed“air regions”and other numerical problems. In this paper a topology opti-mization method based on the method of moments (MoM) for configuration design of planar metallic antenna was pro-posed. The candidate structure of the planar metallic antenna was approximately considered as a resistance sheet with position-dependent impedance. In this way, the electromag-netic property of the antenna can be analyzed easily by using the MoM to solve the radiation problem of the resistance sheet in a finite domain. The topology of the antenna was depicted with the distribution of the impedance related to the design parameters or relative densities. The conductive mate-rial (metal) was assumed to have zero impedance, whereas the non-conductive material was simulated as a material with a finite but large enough impedance. The interpola-tion function of the impedance between conductive material and non-conductive material was taken as a tangential func-tion. The design of planar metallic antenna was optimized for maximizing the efficiency at the target frequency. The results illustrated the effectiveness of the method.     

FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables , was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.     

Comparison of methods for vibration analysis of electrostatic precipitators

The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.     

A novel ellipsoidal acoustic infinite element

A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the eUipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar .to the Burnett‘s method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently, in the examples the infinite elements were considered, excluding the finite elements relative. This novel eUipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.     

FATIGUE GROWTH MODELING OF MIXED-MODE CRACK IN PLANE ELASTIC MEDIA

This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.     

Conservation Law and Application of J-Integral in Multi-Materials

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.     

ANALYSIS OF COMPOSITE LAMINATE BEAMS USING COUPLING CROSS-SECTION FINITE ELEMENT METHOD

Beams and plates manufactured from laminates of composite materials have distinct advantages in a significant number of applications. However, the anisotropy arising from these materials adds a significant degree of complexity, and thus time, to the stress and deformation analyses of such components, even using numerical approaches such as finite elements. The analysis of composite laminate beams subjected to uniform extension, bending, and/or twisting loads was performed by a novel implementation of the usual finite element method. Due to the symmetric features of the deformations, only a thin slice of the beam to be analysed needs to be modelled. Conventional three-dimensional solid finite elements were used for the structural discretization. The accurate deformation relationships were formulated and implemented through the coupling of nodal translational degrees of freedom in the numerical analysis. A sample solution for a rectangular composite laminate beam is presented to show the validity and accuracy of the proposed method.     

Analysis and simulation for tensile behavior of anisotropic open-cell elastic foams

Based on the elongated Kelvin obtained to investigate the tensile behavior Kelvin model＇s periodicity and symmetry in model, a simplified periodic structural cell is of anisotropic open-cell elastic foams due to the whole space. The half-strut element and elastic deflection theory are used to analyze the tensile response as done in the previous studies. This study produces theoretical expressions for the tensile stress-strain curve in the rise and transverse directions. In addition, the theoretical results are examined with finite element simulation using an existing formula. The results indicate that the theoretical analysis agrees with the finite element simulation when the strain is not too high, and the present model is better. At the same time, the anisotropy ratio has a significant effect on the mechanical properties of foams. As the anisotropy ratio increases, the tensile stress is improved in the rising direction but drops in the transverse direction under the same strain.     

Finite cell method compared to h-version finite element method for elasto-plastic problems

The finite cell method （FCM） combines the high-order finite element method （FEM） with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method （h-FEM）. The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.     

Numerical analysis of delamination growth for stiffened composite laminated plates

A study of postbuckling and delamination propagation behavior in delaminated stiffened composite plates was presented. A methodology was proposed for simulating the multi-failure responses, such as initial and postbuckling, delamination onset and propagation, etc. A finite element analysis was conducted on the basis of the Mindlin first order shear effect theory and the von-K6rm~n nonlinear deformation assumption. The total energy release rate used as the criteria of delamination growth was estimated with virtual crack closure technique (VCCT). A self-adaptive grid moving technology was adopted to model the delamination growth process. Moreover, the contact effect along delamination front was also considered during the numerical simulation process. By some numerical examples, the influence of distribution and location of stiffener, configuration and size of the delamination, boundary condition and contact effect upon the delamination growth behavior of the stiffened composite plates were investigated. The method and numerical conclusion provided should be of great value to engineers dealing with composite structures.     

Nonlinear numerical simulation method for galloping of iced conductor

Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.     

PERTURBATION FINITE ELEMENT METHOD FOR SOLVING GEOMETRICALLY NONLINEAR PROBLEMS OF AXISYMMETRICAL SHELL

In analysing the geometrically nonlinear problem of an axisymmetrical thin-walled shell, the paper combines the perturbation method with the finite element method by introducing the former into the variational equation to obtain a series of linear equations of different orders and then solving the equations with the latter. It is well-known that the finite element method can be used to deal with difficult problems as in the case of structures with complicated shapes or boundary conditions, and the perturbation method can change the nonlinear problems into linear ones. Evidently the combination of the two methods will give an efficient solution to many difficult nonlinear problems and clear away some obstacles resulted from using any of the two methods solely. The paper derives all the formulas concerning an axisym-metric shell of large deformation by means of the perturbation finite element method and gives two numerical examples,the results of which show good convergence characteristics.     

ON A NEW KIND OF METHODS TO SOLVE THE PLANE PROBLEMS OF TWO-PHASE FLOW THROUGH POROUS MEDIA

This paper presents a new kind of method for solving the planeproblems of two-phase flow in porous media.The ellipticalpartial differential equation for pressure distribution is sol-ved by the finite element method,and then the semi-analyticalsolution for pressure gradient is used to determine the new sa-turation field according to the existing exact formula describ-ing the saturation propagation along the streamlines.The maindistinguishing feature and advantage of this kind of method arethe ability to overcome the numerical dispersion which is inhe-rent in the ordinary numerical simulation methods.and thereby,to give a precise and clear-cut position of the saturation dis-continuity in the water-oil displacement front.moreover.thesaturation equation,which should commonly be solved simultan-eously or alternatively with the pressure equation,is complete-ly avoided,so that the computing time is greatly reduced.