Wen Chen¹, Hongguang Sun¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.9, No.4, pp. 215-218, 2009, DOI:10.3970/icces.2009.009.215

Abstract This report is to make a survey on the numerical techniques for fractional derivative equations in mechanical and physical fields, including numerical integration of fractional time derivative and emerging approximation strategies for fractional space derivative equations. The perplexing issues are highlighted, while the encouraging progresses are summarized. We also point out some emerging techniques which will shape the future of the numerical solution of fractional derivative equations. More >

R.M. Reddy¹, B.N. Rao²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.4, pp. 149-150, 2009, DOI:10.3970/icces.2009.012.149

Abstract Probabilistic fracture mechanics (PFM) blends the theory of fracture mechanics and the probability theory provides a more rational means to describe the actual behavior and reliability of structures. However in PFM, the fracture parameters and their derivatives are often required to predict the probability of fracture initiation and/or instability in cracked structures. The calculation of the derivatives of fracture parameters with respect to load and material parameters, which constitutes size-sensitivity analysis, is not unduly difficult. However, the evaluation of response derivatives with respect to crack size was a challenging task, since it requires shape sensitivity analysis [1]. Using a brute-force… More >

K. Hashiguchi¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.4, No.4, pp. 257-264, 2007, DOI:10.3970/icces.2007.004.257

Abstract General corotational rate of tensors in arbitrary order having the objectivity is shown first, and then it is verified that the material-derivative of yield condition can be replaced generally to the corotational derivative, i.e. the consistency condition. More >

Cristiano Ubessi¹, Federico C. Buroni^2,*, Gabriel Hattori³, Andrés Sáez⁴, Rogério J. Marczak¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.1, pp. 104-104, 2019, DOI:10.32604/icces.2019.05420

Abstract Efficient three-dimensional infinite Green’s function and its first- and second-order derivatives for materials with piezoelectric coupling are studied in this paper. The procedure is based on an explicit solution recently introduced by the authors which presents three valuable characteristics: (i) it is explicit in terms of the Stroh’s eigenvalues, (ii) it remains well-defined when some Stroh’s eigenvalues are repeated (mathematical degeneracy) or nearly equal (quasi-mathematical degeneracy), and (iii) it is exact. Then, this solution is used to compute coefficients for a double Fourier series representation of the Green’s function and its derivatives. These Fourier expansion representations are realvariable which is… More >

Fei Song¹, Puyou Jia^1,*, Yanan Xiao², Caiying Bo¹, Lihong Hu¹, Yonghong Zhou^1,*

Journal of Renewable Materials, Vol.7, No.10, pp. 1011-1021, 2019, DOI:10.32604/jrm.2019.08044

Abstract Phenolic foams (PFs) as thermal insulation material with outstanding flame retardancy are required to match society’s ever expanding safety expectations; however, a trade off exists between flame retardancy and toughness. Here, for the first time, we synthesized a novel reactive phosphorus containing tung oil based derivative and used it to toughen PF, resulting in PFs with a combination of excellent mechanical properties and flame retardancy. Compared with pure PF, the modified PFs exhibit enhanced mechanical properties, with specific compressive and flexural strengths as high as 5.67 MPa and 12.46 MPa, which represent increases of 90.67% and 178.7% over those of… More >

Nívia do Nascimento Marques¹, Caroline Suzy do Nascimento Garcia¹, Liszt Yeltsin Coutinho Madruga¹, Marcos Antônio Villetti², Men de SáMoreira de Souza Filho³, Edson Noriyuki Ito⁴, Rosangela de Carvalho Balaban^1,*

Journal of Renewable Materials, Vol.7, No.2, pp. 139-152, 2019, DOI:10.32604/jrm.2019.00040

Abstract After industrial mango processing, tons of residues such as peels and kernels are discarded as waste. Nevertheless, almost 60% of the mango kernel is due to starch on a dry weight basis. Herein, starch from mango (Manguifera Indica L.) kernel was applied to obtain a starch fatty ester with vinyl laurate, in DMSO, under basic catalysis. FTIR, 1H and 13C NMR confirmed that a starch ester with a degree of modification of 2.6 was produced. TGA showed that the modified starch has higher thermal stability than its precursors and higher than a vinyl laurate/starch physical blend. SEM data showed that… More >

Zhilin Li^1,∗, Baiying Dong², Fenghua Tong³, Weilong Wang³

CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 63-72, 2019, DOI:10.32604/cmes.2019.04635

Abstract The immersed boundary method is well-known, popular, and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface. In this paper, an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains (exterior or interior) with a Dirichlet boundary condition. The new method inherits the simplicity, robustness, and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives. Numerical examples are provided to confirm the analysis. More >

A.I.Tolstykh, D.A. Shirobokov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 207-222, 2005, DOI:10.3970/cmes.2005.007.207

Abstract A way of using RBF as the basis for PDE's solvers is presented, its essence being constructing approximate formulas for derivatives discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods. Numerical results for different types of elasticity equations showing reasonable accuracy and good$h$-convergence properties of the technique are presented. Applications of the technique to problems with non-self-adjoint operators (like those for the Navier-Stokes equations) are also considered. More >

Zai You Yan^1,2, Fang Sen Cui², Kin Chew Hung²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 97-106, 2005, DOI:10.3970/cmes.2005.007.097

Abstract Taking the normal derivative of solid angles on the surface into account, a modified Burton and Miller's formulation is derived. From which, a more reasonable expression of the hypersingular operator is obtained. To overcome the hypersingular integral, the regularization scheme developed recently is employed. Plane acoustic wave scattering from a rigid sphere is computed to show the correctness of the modified formulation with the regularization scheme. In the computation, eight-nodded isoparametric element is applied. More >

S. Choi¹, M.D. Marcozzi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.3, pp. 201-212, 2004, DOI:10.3970/cmes.2004.005.201

Abstract The general intractability of derivative security pricing models to numerical techniques arguably remains one of the preeminant problems of mathematical finance. In particular, the valuations of such models may be represented as solutions of variational inequalities of evolutionary type typically characterized by their high number of degrees of freedom, unbounded domains, and asymptotic behavior. We consider the application of Multi-Quadratic Radial Basis Functions (MQ-RBF) to the problem of option pricing. More >