Executive Summary : | This project develops a recently proposed numerical algorithm to solve boundary value problems, especially those involving implicit constitutive relations. In this technique, of all the stress fields that satisfy the equilibrium equation and traction boundary condition and the continuous displacement field that satisfy the displacement boundary condition, the one that satisfies the constitutive relation is identified. Since it is computationally possible only to examine a subset of possible fields, the constitutive relation is required to be satisfied in a weak sense. In particular, the Frobenius norm of the error in satisfying the constitutive relation over the entire body is minimized using a sequential quadratic programming algorithm. The main advantages of this technique are (a) applicability to both explicit and implicit constitutive relation (b) equal fidelity in the estimate of displacements and stress (c) the value of the objective function indicates the quality of the approximation obligating the need for error analysis. The main disadvantage is the increase in the number of degrees of freedom in the problem as both the stress and displacement fields are taken as primary unknowns. However, the algorithm is embarrassingly parallelizable, and hence, the computational wall time would reduce by parallelizing the code. Also, the core of the present technique is multivariate function minimizer subject to linear or nonlinear constraint compared to linear algebraic equation solver in the classical finite element technique. Therefore a new software architecture is required for this technique. Thus, the aim of this project are (a) to extend the recently proposed numerical technique for viscoelastic and plastic constitutive relation, (b) to study the plane Boussinesq problem and beam analysis for nonlinear elastic or inelastic constitutive relation in detail which may lead to a better design of pavement and reinforced concrete beams, (c) to implement a parallelized software framework for the numerical technique in such a manner that it would allow addition of elements, analysis methods and constitutive relations. |
Co-PI: | Prof. Sathya Peri Indian Institute Of Technology Hyderabad, Telanganaa,Kandi,Telangana,Sangareddy-502284, Dr. Syed Nizamuddin Khaderi Indian Institute Of Technology Hyderabad, Telanganaa,Kandi,Telangana,Sangareddy-502284 |