Isogeometric analysis of linear isotropic and kinematic hardening elastoplasticity

Abstract

Abstract. Material nonlinearity is of great importance in many engineering problems. In this paper, we exploit NURBS-based isogeometric approach in solving materially nonlinear problems, i.e. elastoplastic problems. The von Mises model with linear isotropic hardening and kinematic hardening is presented, and furthermore the method can also be applied to other elastoplastic models without any loss of generality. The NURBS basis functions allow us to describe exactly the curved geometry of underlying problems and control efficiently the accuracy of approximation solution. Once the discretized system of non-linear equilibrium equation is obtained, the Newton-Raphson iterative scheme is used. Several numerical examples are tested. The accuracy and reliability of the proposed method are verified by comparing with results from ANSYS Workbench software.

An enhanced nodal gradient finite element for non-linear heat transfer analysis

“…the initial condition, temperature at any given time steps within the time domain can be solved. Solution of the nonlinear equation 13is then obtained using the iterative Newton-Raphson scheme (see [16,17]). Convergence is achieved when the residual evaluated in Eq.…”

“…It is expected that the cylinder will be gradually heated from the inner wall to the outer wall. The dependency of specific heat capacity [16] and thermal conductivity [17] on temperature from 400 K to 600 K is presented in Table 1. Values that are not found in Table 1 will be linearly interpolated.…”

“…Substitution of Eqs. (15)- (17) into Eq. (12) and approximate the time derivative of temperature using Eq.…”

Isogeometric Analysis of Soil Plasticity

“…The use of isogeometric collocation has shown potential to increase the computational efficiency of the isogeometric framework, outperforming both the standard Galerkin form of isogeometric analysis and standard C 0 finite element analysis with regard to computational costs [7]. As pointed out by Nguyen et al [12] for nonlinear analysis the numerical error strongly depends on the integration scheme and the order of the Non-Uniform Rational B-splines (NURBS) basis functions.…”