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Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids |
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| Authors: | J Sladek V Sladek Ch Zhang M Schanz |
| Affiliation: | (1) Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia;(2) Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany;(3) Institute of Applied Mechanics, Graz University of Technology, A-8010 Graz, Austria |
| Abstract: | A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of quasi-static and transient dynamic problems in two-dimensional (2-D) nonhomogeneous linear viscoelastic media. A unit step function is used as the test functions in the local weak form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The correspondence principle is applied to such nonhomogeneous linear viscoelastic solids where relaxation moduli are separable in space and time variables. Then, the LBIEs are formulated for the Laplace-transformed viscoelastic problem. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-D problems. The moving least squares (MLS) method is used for approximation of physical quantities in LBIEs. |
| Keywords: | Meshless method Local weak form Correspondence principle Moving least squares interpolation Laplace transform Functionally graded materials Viscoelasticity |
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