HYBRID FEM WITH FUNDAMENTAL SOLUTIONS AS TRIAL FUNCTIONS FOR HEAT CONDUCTION SIMULATION

A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.

A mathematical model of cortical bone remodeling at cellular level under mechanical stimulus

A bone cell population dynamics model for cor- tical bone remodeling under mechanical stimulus is devel- oped in this paper. The external experiments extracted from the literature which have not been used in the creation of the model are used to test the validity of the model. Not only can the model compare reasonably well with these ex- perimental results such as the increase percentage of final values of bone mineral content （BMC） and bone fracture en- ergy （BFE） among different loading schemes （which proves the validity of the model）, but also predict the realtime devel- opment pattern of BMC and BFE, as well as the dynamics of osteoblasts （OBA）, osteoclasts （OCA）, nitric oxide （NO） and prostaglandin E2 （PGE2） for each loading scheme, which can hardly be monitored through experiment. In conclusion, the model is the first of its kind that is able to provide an in- sight into the quantitative mechanism of bone remodeling at cellular level by which bone cells are activated by mechan- ical stimulus in order to start resorption/formation of bone mass. More importantly, this model has laid a solid foun- dation based on which future work such as systemic control theory analysis of bone remodeling under mechanical stimu- lus can be investigated. The to-be identified control mecha- nism will help to develop effective drugs and combined non- pharmacological therapies to combat bone loss pathologies. Also this deeper understanding of how mechanical forces quantitatively interact with skeletal tissue is essential for the generation of bone tissue for tissue replacement purposes in tissue engineering.

Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials （FGMs）. First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest＇s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

Three Boundary Meshless Methods for Heat Conduction Analysis in Nonlinear FGMs with Kirchhoff and Laplace Transformation

This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of fundamental solution(MFS),the boundary knot method(BKM),and the collocation Trefftz method(CTM)in conjunction with Kirchhoff transformation and various variable transformations.In the analysis,Laplace transform technique is employed to handle the time variable in transient heat conduction problem and the Stehfest numerical Laplace inversion is applied to retrieve the corresponding time-dependent solutions.The proposed MFS,BKM and CTM are mathematically simple,easyto-programming,meshless,highly accurate and integration-free.Three numerical examples of steady state and transient heat conduction in nonlinear FGMs are considered,and the results are compared with those from meshless local boundary integral equation method(LBIEM)and analytical solutions to demonstrate the effi-ciency of the present schemes.

Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics

With the rapid development of computer technology,numerical simulation has become the third scientific research tool besides theoretical analysis and experi-mental research.As the core of numerical simulation,constructing efficient,accurate and stable numerical methods to simulate complex scientific and engineering prob-lems has become a key issue in computational mechanics.The article outlines the ap-plication of singular boundary method to the large-scale and high-frequency acoustic problems.In practical application,the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency soundfield.This article focuses on the following two research areas.They are how to discretize partial differential equations into more appropriate linear equations,and how to solve linear equations more efficiently.The bottle neck problems encountered in the compu-tational acoustics are used as the technical routes,i.e.,efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies.The article reviews recent advances in emerging appli-cations of the singular boundary method for computational acoustics.This collection can provide a reference for simulating other more complex wave propagation.

A DAMAGE MECHANICS MODEL FOR TWISTED CARBON NANOTUBE FIBERS

Carbon nanotube fibers can be fabricated by the chemical vapor deposition spinning process. They are promising for a wide range of applications such as the building blocks of high-performance composite materials and micro-electrochemical sensors. Mechanical twisting is an effective means of enhancing the mechanical properties of carbon nanotube fibers during fabrication or by post processing. However, the effects of twisting on the mechanical properties remain an unsolved issue. In this paper, we present a two-scale damage mechanics model to quantitatively investigate the effects of twisting on the mechanical properties of carbon nanotube fibers. The numerical results demonstrate that the developed damage mechanics model can effectively describe the elastic and the plastic-like behaviors of carbon nanotube fibers during the tension process. A definite range of twisting which can effectively enhance the mechanical properties of carbon nanotube fiber is given. The results can be used to guide the mechanical twisting of carbon nanotube fibers to improve their properties and help optimize the mechanical performance of carbon nanotube-based materials.