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This paper presents a new damage detection and localization technique based on the changes in vibration parameters using BAT and Particle Swarm Optimization algorithm. The finite element method is used to apply damage at specific element(s) of the considered beams. The damage is represented by a reduction in Young's modulus and the identification of damage is formulated as an optimization problem using objective function based on Modal Scale Factor and changes in natural frequencies. A procedure for detecting and locating damage of beam-like structures based on BAT algorithm is used. This approach presents a method that can be used to detect the single and multiple-damage positions and the rate of damage in structural elements with high accuracy after the first iteration. The results obtained using BAT algorithm are compared to those obtained using Particle Swarm Optimization Algorithm. By taking noise into account in the damage detection and localization problem, it is shown that our approach based on BAT algorithm can detect the damage locations with high accuracy.

Analysis-suitable T-splines are used for the modeling and analyzing of cracks in bimaterial interfaces within the framework of an extended isogeometric analysis (XIGA). The crack tip enrichment functions of bimaterial interface cracks are implemented to reproduce singular fields, and the signed distance functions are used to treat the crack face and the interface in the models. A compatible local refinement algorithm is applied to refine location of the crack and the interface, which helps one to avoid produce excessive propagation of control points. The mixed mode stress intensity factors (SIFs) which are evaluated by the interaction integral (M-integral) are used as analysis parameters. Numerical simulations are performed to analyze the problem and to examine the efficiency of the proposed method. The obtained results are compared with other available results.

Colloque avec actes et comité de lecture. Internationale.; International audience; In this paper, a meshfree cell-based smoothed radial point interpolation method (CS-RPIM) is extended to large-deformation elasto-visco-plasticity analysis for simulation of high speed sheet metal blanking processes. For this purpose, two techniques included in large-deformation analysis formulation are employed: a Johnson?Cook flow stress model and an updated Lagrangian scheme to integrate the constitutive relations. The volumetric locking due to the nearly incompressible behavior of elastic-visco-plastic deformations is remedied by relaxing the volumetric strain through the mean value computed by the strain smoothing approach coupled with the meshfree radial point interpolation method (RPIM) (based on the radial basis functions interpolation). The next step concern the description of ductile fracture initiation and propagation, which is essential to predict final product shapes in the blanking process. A hybrid approach is elaborated combining a damage model, based on a failure criterion for the brittle mode initiation; assumed to initiate when the maximum tensile principal stress at a node reaches a critical value, and a stress intensity factor model, to handle the crack propagation calculations once the crack opening is already created. The proposed algorithm duplicates cutting nodes that meet specific conditions and avoid the global remeshing procedure. Validity of the CS-RPIM for large-deformation metal forming problem is proved by benchmarks, and numerical example of sheet metal blanking process. Obtained results demonstrates that, the proposed method possess superior accuracy and convergence properties for strain energy solutions comparing to the standard FEM, the combination of the strain smoothing approach with the powerfull RPIM technique can easily simulate problems with severe element distortion, and solve volumetric locking problem in large-deformation analysis.

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole, {"references":["P. Metsis, N. Lantzounis, M. Papadrakakis. A new hierarchical partition of unity formulation of EFG meshless methods. Computer Methods in Applied Mechanics and Engineering, 2015, vol 283, pp 782-805.","T.R. Chandrupatla and A.D. Belegundu, \"Introduction to Finite Element in Engineering\" 2002, Ed. 3rd.","C.V. Le, H. Askes, M. Gilbert, Adaptive element-free Galerkin method applied to the limit analysis of plates, Comput. Methods Appl. Mech. Engrg. 199 (37–40) (2010) 2487–2496.","Zhu T and Atluri SN, A modified collocation a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput. Mech., 21, pp 211-222. 2007.","Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. method: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 13.","Atluri SN, Zhu T (2000) The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics. Comput. Mech. 25: pp169–179.","Liu W. K. Li S, Belytschko T, Moving least square reproducing kernel method (I) methodology and convergence. Comput. Meth. Eng. 1997.","T. Belytschko, Y.Y. Lu, L. Gu, \"Element-free Galerkin methods\". International Journal of Numerical Methods in Engineering, 1994, vol. 37, pp. 229-256.","J. S. Chen, C. T. Wu, S. Yoon, Y. You, \"A Stabilized conforming nodal integration for galerkin mesh free methods\", International Journal of Numerical Methods in Engineering, 2001, vol. 50, pp. 435-466.\n[10]\tHua Li, Shantanu S. Mulay. Meshless Method and their numerical proprieties. CRC Press, Taylor and Francis Group, 2013. \n[11]\tY. Zhang, M. Xia, Y. Zhai, \"Analyzing Plane-plate Bending with EFGM\", 2009, Journal of Mathematics Research, vol.-1, no-1. \n[12]\tP. Soparat, P. Nanakorn,\" Analysis of crack growth in concrete by the element freegalerkin method\", pp. 42-46.\n[13]\tNayroles B., Touzot G., Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational mechanics, 1992, 10: 307–318.\n[14]\tDolbow J, Belytschko T., An Introduction to Programming the Meshless Element Free Galerkin Method, Archives of Computational Methods in Engineering, 5(3), 207-241 (1998).\n[15]\tBui Manh Tuan, Chen Yun Fei. Analysis and prediction of crack propagation in plates by the enriched free Galerkin method. International Journal of Mechanical Engineering and Applications, 2014; 2(6): 78-86.\n[16]\tTimoshenko SP, Goodier JN. Theory of elasticity. 3rd ed. New York: McGraw-hill; 1970.\n[17]\tANSYS User's Guide, Revision 12.0 Tutorials, Swanson Analysis System, 2014."]}

In this work the advances in meshfree methods, partic- ularly the Radial Basis Function based meshfree Galerkin Methods, are presented with the purpose of analyzing the performance of their meshless approximations and integration techniques. The Radial Point Interpolation Method (RPIM) is studied based on the global Galerkin weak form performed using classical Gaussian integration and the stabilized conforming nodal integration scheme. The numeri- cal performance of this category of methods is tested on their behavior on two elastic problems with regular node grids, and two other with distorted irregular grids. All RPIM methods perform very well in term of elastic computation, the Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node schemes. Keywords—adial Basis Function Radial Point Interpolation Method Galerkin weak form Nodal Integrationadial Basis Function Radial Point Interpolation Method Galerkin weak form Nodal Integration.