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WSEAS TRANSACTIONS on
APPLIED and THEORETICAL MECHANICS

Issue 12, Volume 2, December 2007
Print ISSN: 1991-8747
E-ISSN: 2224-3429

Title of the Paper: Mathematical Modeling of the Intervertebral Disc as an Infrastructure for Studying the Mechanobiology of the Tissue Engineering Procedure

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Authors: Mohammad Haghpanahi, Mohammad Nikkhoo, Habiballah Peirovi and Jalal-Edin Ghanavi

Abstract: Mechanical stress has a significant influence on the residing cells in the intervertebral disc and we can nominate it as one of the principle fields of researches in tissue engineering. So it is very important to propose a suitable model as an infrastructure for a better understanding of the mechanobiology of the intervertebral disc. This paper presents a novel finite element formulation which can be used in our predicted tissue engineering procedure as a powerful model. After derivation of the governmental equations, the standard Galerkin weighted residual method was used to form the finite element model. Then the implicit time integration schemes were applied to solve the nonlinear equations. The formulation accuracy and convergence for 1D case were examined with Sun's and Simon's analytical solution and also Drost's experimental Data. It is shown that the mathematical model is in excellent agreement and has the capability to simulate the intervertebral disc response under different types of mechanical and electrochemical loading conditions. At the end, to have a short review of the capability of the model, three main exemplary problems are proposed. So in this case, investigation of the role of porosity in scaffold manufacturing, effect of FCD and water content on mechanical response and also the nutrition criterion in IVD tissue engineering procedure are discussed.

Keywords: Finite element modeling, Porous media, Intervertebral disc, Mechanobiology, Tissue engineering

Title of the Paper: Limit Analysis of Stability of Circular Foundation Pit

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Authors: Cui Xinzhuang, Yao Zhanyong, Jin Qing and Wu Shimei

Abstract: Circular foundation pits often appear in civil engineering. In order to obtain the critical depth of the non-supported circular foundation pit, the upper-bound method in plasticity mechanics was employed. The assumed slip surface in analysis was the rotational logspiral surface. The kinematically admissible velocity field was obtained according to the associated flow rule for Coulomb material, and the optimization model of the critical depth was established and solved with SQP optimization algorithm. The variations of the critical depth with the slope angle, the ratio of depth to radius of pit and the internal friction angle of soil were studied. The arch effect of the circular foundation pit makes the critical depth larger than the critical height of the plane slope; however, when the ratio of depth to radius of pit approaches zero, the upper-bound solution of the former approaches that of the latter. If the ratio of depth to diameter of pit is less than 10, the arch effect may be ignored and the foundation pit can be analyzed as the plane slope with the method of slices. Comparisons between upper-bound solution(UBS), the solution from approximate slip line theory(SLS) and finite difference solution(FDS) showed that UBS is less than SLS and larger slightly than FDS.

Keywords: circular foundation pit; slope; critical depth; limit analysis; upper-bound method; arch effect