Structural analysis of viscoelastic solid polymers is one of the most important subjects in engineering structures. Several attempts have been so far made for the integral equation approach to viscoelastic problems. From the basic assumptions of viscoelastic constitutive equations and weighted residual techniques, a simple but effective boundary element formulation (BEF) is implemented for the standard linear solid (SLS) viscoelastic models. The SLS model provides an approximate representation of the observed behavior of a real polymer in its viscoelastic range. This formulation needs only Kelvin’s fundamental solution of isotropic elastostatics with material constants prescribed as explicit functions of time. This approach avoids the use of relaxation functions and mathematical transformations, and it is able to solve the quasistatic viscoelastic problems with any load time-dependence and boundary conditions. As an application, a numerical example is provided to validate the proposed formulation. The problem of the pressurization of thick-walled cylindrical viscoelastic tanks made of PMMA polymer is completely analyzed by this approach.
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Ashrafi, H., Farid, M. A mathematical boundary integral equation analysis of standard viscoelastic solid polymers. Comput Math Model 20, 397–415 (2009). https://doi.org/10.1007/s10598-009-9046-x
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DOI: https://doi.org/10.1007/s10598-009-9046-x