Numerical techniques for solving truss problems involving viscoelastic materials

• Published in: International journal of non-linear mechanics Vol. 122; p. 103479
• Main Authors: Ananthapadmanabhan, S, Saravanan, U
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.06.2020; Elsevier BV
• Subjects: Boundary conditions; Computer simulation; Constitutive relationships; Creep (materials); Displacement; Equilibrium equations; Finite element method; Independent variables; Integral type; Mathematical models; Rate type; Truss analysis; Trusses; Viscoelastic materials; Viscoelasticity; Viscoelasticity; Rate type; Truss analysis; Integral type
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2020.103479

We develop a methodology for solving truss problems involving viscoelastic materials where, of all the member forces that satisfy the nodal force equilibrium equation and nodal displacements that satisfy the displacement boundary conditions, those member forces and nodal displacements that satisfy the constitutive relation are sought. Since a rate type viscoelastic constitutive relation involves the rate of the stress or strain, this study explores the use of member forces, nodal displacements, and support reactions or their rates as independent variables. Assuming small deformations, the nodal force equilibrium and the displacement boundary condition results in a linear equality constraint between the independent variables. Then we find the unknown independent variables such that the root mean squared error in the constitutive relation of the members of the truss is minimized subject to the satisfaction of the linear constraint at selected times. The objective function is evaluated at selected times or integrated over subintervals of time. We explore six possible solution methods and benchmark them for their accuracy and efficiency. We study statically determinate and indeterminate truss whose members are modeled using rate and integral type viscoelastic constitutive relations for creep and oscillatory loading. For the standard linear solid model, we find that the proposed methods are more accurate than ABAQUS and, at times, require lesser computational wall time. We also demonstrate the applicability of the proposed methodology to fractional order and nonlinear viscoelastic constitutive relations. •Applies a recently proposed formulation to solve viscoelastic boundary value problems.•Analyze trusses made of viscoelastic material.•Possibility of using either rate or integral type constitutive relations.•Accurate and faster convergence than ABAQUS solution.