of Nonlinear Partial Differential Equations: Further Development of the Methodology with Applications. Applied Mathematics and Computation, 269 (2015), 363-378.  M urray , J. D. Lectures on Nonlinear Differential Equation Models in Biology, Oxford, Oxford University Press, 1977.  A blowitz , M., P. A. C larkson . Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge, Cambridge University Press, 1991.  V itanov , N. K. Science Dynamics and Research Production. Indicators, Indexes, Statistical Laws and Mathematical
Nikolay K. Vitanov and Zlatinka I. Dimitrova
Sangamesh Gondegaon and Hari K. Voruganti
. HUGHES. An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS, immersed Boundary Methods, and T-spline CAD Surfaces. Computer Methods in Applied Mechanics and Engineering, 249 (2012), 116-150.  WALL, W. A., M. A. FRENZEL, C. CYRON. Isogeometric Structural Shape Optimization. Computer Methods in Applied Mechanics and Engineering, 197 (2008), No. 33, 2976-2988.  HASSANI, BEHROOZ, S. M. TAVAKKOLI, N. Z. MOGHADAM. Application of Isogeometric Analysis in Structural Shape Optimization
Sangamesh Gondegaon and Hari K. Voruganti
Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no self-intersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.
Kavan Khaledi, Tom Schanz and Shorash Miro
Complex engineering problems require using computation- ally expensive simulations which take relatively long time. In such cases, routine tasks such as design optimization, parameter identification, or sensitivity analysis become impractical since they require thousands or even millions of simulations. A common practice for engineers to solve this problem is to use metamodels in place of actual simulation models. In this paper, we investigate the performance of four metamodelling approaches, namely, Response Surface Methodology, Moving Least Squares, POD-RBF, and Neighborhood Approximation considering the effect of sample size and sampling methods. Our main goal in this work is to find a reliable and robust metamodel technique in order to construct an approximated function for mechanized tunnel simulation. For this reason, a numerical study is carried out on a 3D tunnel modeled in Plaxis3D and the accuracy and robustness of the aforementioned metamodelling techniques are discussed
Tsviatko V. Rangelov, Petia S. Dineva and George D. Manolis
The aim of this study is to develop an efficient numerical technique using the non-hypersingular, traction boundary integral equation method (BIEM) for solving wave propagation problems in an anisotropic, viscoelastic plane with cracks. The methodology can be extended from the macro-scale with certain modifications to the nano-scale. Furthermore, the proposed approach can be applied to any type of anisotropic material insofar as the BIEM formulation is based on the fundamental solution of the governing wave equation derived for the case of general anisotropy. The following examples are solved: (i) a straight crack in a viscoelastic orthotropic plane, and (ii) a blunt nano-crack inside a material of the same type. The mathematical modelling effort starts from linear fracture mechanics, and adds the fractional derivative concept for viscoelastic wave propagation, plus the surface elasticity model of M. E. Gurtin and A. I. Murdoch, which leads to nonclassical boundary conditions at the nano-scale. Conditions of plane strain are assumed to hold. Following verification of the numerical scheme through comparison studies, further numerical simulations serve to investigate the dependence of the stress intensity factor (SIF) and of the stress concentration factor (SCF) that develop in a cracked inhomogeneous plane on (i) the degree of anisotropy, (ii) the presence of viscoelasticity, (iii) the size effect with the associated surface elasticity phenomena, and (iv) finally the type of the dynamic disturbance propagating through the bulk material.
Valentin Abadjiev and Haruhisa Kawasaki
The computer design has improved forming different type software for scientific researches in the field of gearing theory as well as performing an adequate scientific support of the gear drives manufacture. Here are attached computer programs that are based on mathematical models as a result of scientific researches. The modern gear transmissions require the construction of new mathematical approaches to their geometric, technological and strength analysis. The process of optimization, synthesis and design is based on adequate iteration procedures to find out an optimal solution by varying definite parameters.
The study is dedicated to accepted methodology in the creation of soft- ware for the synthesis of a class high reduction hyperboloid gears - Spiroid and Helicon ones (Spiroid and Helicon are trademarks registered by the Illinois Tool Works, Chicago, Ill). The developed basic computer products belong to software, based on original mathematical models. They are based on the two mathematical models for the synthesis: “upon a pitch contact point” and “upon a mesh region”. Computer programs are worked out on the basis of the described mathematical models, and the relations between them are shown. The application of the shown approaches to the synthesis of commented gear drives is illustrated.
P. Dineva, S. Parvanova, G. Vasilev and F. Wuttke
Two-dimensional elastodynamic problem for seismic response of unlined and lined tunnels located in a layered half-plane with free surface relief is solved. The computation tool uses the idea of the global matrix propagator method which allows derivation of a relation between the wave field quantities along different interfaces in the layered half- plane. The numerical realization of this idea is performed with the help of the sub-structured boundary element method (BEM) well suited when objects with arbitrary geometry are considered. A relation between dis- placements and tractions along the free surface and arbitrary interface of the soil stratum is derived. It works for arbitrary geometry of the interfaces between soil layers. Finally, in the companion paper, numerical results are presented which show both a validation study of the pro- posed computational methodology and extensive numerical simulations demonstrating the influence of some important factors as type and characteristics of the incident wave, dynamic tunnels interaction, soil-tunnel interaction, free surface relief, type of the tunnel construction and mechanical properties of the layered half-plane on the complex seismic field near and far-away from the underground structures.
Rumiana Kotsilkova, Irena Borovanska, Peter Todorov, Evgeni Ivanov, Dzhihan Menseidov, Sudip Chakraborty and Chiranjib Bhattacharjee
References  A luwi S hakir , N. A., K. Y. W ong , M. Y. N oordin , I. S udin . Development of a High Performance PES Ultrafiltration Hollow Fiber Membrane for Oily Wastewater Treatment Using Response Surface Methodology. Sustainability , 18 (2015), 16465-16482.  P raneeth , K. Synthesis and Characterization of Novel Polymeric Membranes for Water Purification and Effluents Treatment, PhD thesis, RMIT University, Australia, 2014.  S umisha , A., G. A rthanareeswaran , Y. L ukkathuyavan , A. F ismail , S. C hakraborty . Treatment of
A. Maleki and A. Ahmadi
Imperfection Sensitivity of Unstiffened CFRP Cylindrical Shells. Composite Structures , 92 (2010), 1939-1946.  L ee , M. C. W., R. M. P ayne , D. W. K elly , R. S. T homson . Determination of Robustness for a Stiffened Composite Structure Using Stochastic Analysis. Composite Structures , 86 (2008), 78-84.  O rifici , A. C., R. S. T homson , R. D egenhardt , C. B isagni , J. B ayandor . A Finite Element Analysis Methodology for Analyzing Degradation and Collapse in Postbuckling Composite Aerospace Structures. Journal of Composite Materials , 43
Dimitar Chakarov, Ivanka Veneva, Mihail Tsveov and Pavel Venev
(2007), No. 3 , 549-573.  D avis , J., J. C anderle , P. A rtrit , N. T sagarakis , D. G. C aldwell . Enhanced Dynamic Performance in Pneumatic Muscle Actuators, Pros. of the 2002 IEEE ICRA, DOI: 10.1109/ROBOT.2002.1013662, 2002, 2836-2841.  S hin , D., X. Y eh , O. K hatib . Variable Radius Pulley Design Methodology for Pneumatic Artifical Muscle-based Antagonistic Actuation Systems, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, September 25–30, 2011, USA, CA, San Francisco, 2011, 1830-1835.  S ardellitti , I