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

Acta Mechanica Sinica 2012年第6期28卷 1678-1692页

作者： qing-hua qin Ya-Nan Wang Research School of Engineering The Australian National University

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.

关键词： Cortical bone remodeling Cell population dy-namics Mechanotransduction Mechanosensitivity Bonefracture energy - Bone mineral content

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

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Acta Mechanica Solida Sinica 2009年第5期22卷 487-498页

作者： Hui Wang qing-hua qin College of Civil Engineering and Architecture Henan University of Technologyl Zhengzhou 450052 China Department of Engineering Australian National University Canberra ACT 0200 Australia

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.

关键词： hybrid FEM fundamental solution variational functional heat conduction

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Parametric study of control mechanism of cortical bone remodeling under mechanical stimulus

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Acta Mechanica Sinica 2010年第1期26卷 37-44页

作者： YananWang qing-hua qin Department of Engineering Australian National UniversityCanberra ACT 0200 Australia

The control mechanism of mechanical bone remodeling at cellular level was investigated by means of an extensive parametric study on a theoretical model described in this paper. From a perspective of control mechanism, it was found that there are several control mechanisms working simultaneously in bone remodeling which is a complex process. Typically, an extensive parametric study was carried out for investigating model parameter space related to cell differentiation and apoptosis which can describe the fundamental cell lineage behaviors. After analyzing all the combinations of 728 permutations in six model parameters, we have identified a small number of parameter combinations that can lead to physiologically realistic responses which are similar to theoretically idealized physiological responses. The results presented in the work enhanced our understanding on mechanical bone remodeling and the identified control mechanisms can help researchers to develop combined pharmacological-mechanical therapies to treat bone loss diseases such as osteoporosis.

关键词： Control mechanism Parametric study Mechanical bone remodeling

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FUNDAMENTAL SOLUTION BASED GRADED ELEMENT MODEL FOR STEADY-STATE HEAT TRANSFER IN FGM

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Acta Mechanica Solida Sinica 2012年第4期25卷 377-392页

作者： Leilei Cao Hui Wang qing-hua Qi Key Laboratory for Highway Construction Technology and Equipment of Ministry of Education Chang'an University Xi'an 710064 China School of Engineering Australian National University canberra ACT 0200 Australia College of Civil Engineering and Architecture Henan University of Technology Zhengzhou 450052 China

A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials （FGMs）. The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the interelement boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element （FE） model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional FEM and boundary element method （BEM）. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.

关键词： graded element hybrid FEM heat conduction functionally graded materials

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

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Acta Mechanica Sinica 2012年第1期28卷 128-139页

作者： Lei-Lei Cao qing-hua qin Ning Zhao Key Laboratory for Road Construction Technology＆ Equipment of MOE Chang＇ an University 710064 Xi＇ an China Research School of Engineering Australian National UniversityCanberra ACT 0200 Australia School of Mechatronics Northwestern Polytechnical University710072 Xi＇an China

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.

关键词： Graded element model Functionally graded materials Hybrid FEM Transient heat conduction

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

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Advances in Applied Mathematics and Mechanics 2012年第5期4卷 519-542页

作者： Zhuo-Jia Fu Wen Chen qing-hua qin Center for Numerical Simulation Software in Engineering and Sciences Department of Engineering MechanicsHohai UniversityNanjingJiangsuP.R.China Research School of Engineering Building 32Australian National UniversityCanberraACT 0200Australia

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 *** 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 *** proposed MFS,BKM and CTM are mathematically simple,easyto-programming,meshless,highly accurate and *** 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.

关键词： Method of fundamental solution boundary knot method collocation Trefftz method Kirchhoff transformation Laplace transformation meshless method

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A DAMAGE MECHANICS MODEL FOR TWISTED CARBON NANOTUBE FIBERS

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Acta Mechanica Solida Sinica 2012年第4期25卷 342-347页

作者： qingqing Rong Jianshan Wang Yilan Kang Yali Li qing-hua qin Tianjin Key Laboratory of Modern Engineering Mechanics Department of MechanicsSchool of Mechanical EngineeringTianjin UniversityTianjin 300072China Key Laboratory of Advanced Ceramics and Machining Technology Ministry capable of EducationSchool of Materials Science and EngineeringTianjin UniversityTianjin 300072China School of Engineering Australian National UniversityCanberraACT 0200Australia

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.

关键词： carbon nanotube fibers damage twisting, multi-level structures elastic modulus

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

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 315-343页

作者： Junpu Li Zhuojia Fu Yan Gu qing-hua qin School of Mechanics and Safety Engineering Zhengzhou UniversityZhengzhouHenan 450001China College of Mechanics and Materials Hohai UniversityNanjingJiangsu 211100China College of Mathematics Qingdao UniversityQingdaoShandong 266071China College of Engineering and Computer Science Australian National UniversityCanberra ACT 2601Australia

With the rapid development of computer technology,numerical simulation has become the third scientiﬁc research tool besides theoretical analysis and experi-mental *** 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 *** article outlines the ap-plication of singular boundary method to the large-scale and high-frequency acoustic *** practical application,the key issue is to construct efﬁcient and accurate numerical methodology to calculate the large-scale and high-frequency soundﬁ*** article focuses on the following two research *** are how to discretize partial differential equations into more appropriate linear equations,and how to solve linear equations more efﬁ*** 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 *** article reviews recent advances in emerging appli-cations of the singular boundary method for computational *** collection can provide a reference for simulating other more complex wave propagation.

关键词： Singular boundary method origin intensity factor high-frequency acoustic problems large-scale acoustic problems Helmholtz equation

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Morphological stability analysis of vesicles with mechanical-electrical coupling effects

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Acta Mechanica Sinica 2010年第1期26卷 5-11页

作者： Lingtian Gao Ying Liu ~ qing hua qin~* Xi Qiao Feng Applied Mechanics Lab Department of Engineering Mechanics Tsinghua University 100084 Beijing China Institute of Mechanics Beijing Jiaotong University 100044 Beijing China Department of Engineering The Australian National UniversityCanberra ACT 0200 Australia

Using a recently established liquid crystal model for vesicles, we present a theoretical method to analyze the morphological stability of liquid crystal vesicles in an electric field. The coupled mechanical-electrical effects associated with elastic bending, osmotic pressure, surface tension, Max- well pressure, as well as flexoelectric and dielectric proper- ties of the membrane are taken into account. The first and second variations of the free energy are derived in a com- pact form by virtue of the surface variational principle. The former leads to the shape equation of a vesicle embedded in an electric field, and the latter allows us to examine the stabil- ity of a given vesicle morphology. As an illustrative exam- ple, we analyze the stability of a spherical vesicle under a uniform electric field. This study is helpful for understanding and revealing the morphological evolution mechanisms of vesicles in electric fields and some associated phenomena of cells.

关键词： Vesicle Cell membrane - Stability Mechanical-electrical coupling

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Escape probability for isotropic emitters near Kerr black hole with astrometric

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Communications in Theoretical Physics 2024年第5期76卷 128-133页

作者： Yu-Xuan Han qing-hua Zhu qing-Guo huang CAS Key Laboratory of Theoretical Physics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China School of Physical Sciences University of Chinese Academy of SciencesNo.19A Yuquan RoadBeijing 100049China Department of Physics Chongqing UniversityChongqing 401331China School of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced Study UCASHangzhou 310024China

The paper investigates the escape probability for isotropic emitters near a Kerr black *** propose a new approach to obtain the escape probability in a general manner,going beyond previous case-by-case *** approach is based on studies of the black hole shadow with astrometric observable and can be applied to emitters with an arbitrary 4-velocities and locations,even to the emitters outside of the equatorial *** also consider representative examples illustrating how escape probabilities vary with distance,velocity,and inclination ***,this new approach provides an effective method for studying escape probabilities near Kerr black holes.

关键词： Kerr black hole photon escape probability isotropic emitters

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