Context Of Isogeometric Analysis Research Articles

Large deformation frictional contact formulations for isogeometric Kirchhoff–Love shell

The large deformation frictional contact between shell structures is commonplace in engineering applications like the sheet metal forming process. Due to the specific assumptions of shell structures, the numerical calculation of shell contact is more complicated than the computation of contact between normal two or three dimensional solids. In recent years, the Kirchhoff–Love shell has become one of the most popular mathematical shell models under the context of isogeometric analysis. In this paper, we detailedly formulate the frictional contact contributions for Kirchhoff–Love shell structures considering both stick and slide states. The variation and linearization of contact variables considered to be sophisticated are explicitly derived and plainly organized. The general nonlinear hyperelastic materials are utilized to describe the constitutive relations of shell structures undergoing large deformation. The normal and tangential contact constraints are enforced using the classical penalty method. Based on the precise representation of shell structures using NURBS functions, we developed an effective contact detection algorithm to accurately capture the contact areas between shells. A computation framework for solving Kirchhoff–Love shell frictional contact problems is established in the context of NURBS-based isogeometric analysis. Several shell contact examples are calculated, and the obtained results are compared with those of the classical finite element method. The convergence and accuracy of the presented method are verified in these examples.

Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory

A novel and effective computational approach within the context of isogeometric analysis (IGA) is developed for analyzing size-dependent mechanical behaviors of functionally graded (FG) microbeams. To capture the size effects, an extension of quasi-3D theory is established to integrate with the modified couple stress theory. The nonuniform rational B-spline (NURBS) basis functions are employed and can directly meet the first-order derivative demand of the quasi-3D theory, where four variables are involved at each node. In this new setting, both normal and shear deformations are considered, while the shear correction factor is avoided. Numerical examples are studied, in which the effects of several factors, including material gradient factor, boundary conditions, parameter of material length scale, and aspect ratio, on deflections, stresses, and fundamental frequencies of FG microbeams are explored.

Shape optimization and optimal control for transient heat conduction problems using an isogeometric approach

This work is concerned with the development of a framework to solve shape optimization problems for transient heat conduction problems within the context of isogeometric analysis (IGA). A general objective functional is used to accommodate both shape optimization and passive control problems under transient conditions. An adjoint sensitivity analysis, which accounts for possible discontinuities in the objective functional, is performed analytically and subsequently discretized within the context of IGA. The gradient of the objective functional is used in a descent algorithm to solve optimization problems. Numerical examples are presented to validate and demonstrate the capacity to manage thermal fields under transient conditions.

Isogeometric shape optimization for quasi-static processes

Summary A framework to solve shape optimization problems for quasi-static processes is developed and implemented numerically within the context of isogeometric analysis (IGA). Recent contributions in shape optimization within IGA have been limited to static or steady-state loading conditions. In the present contribution, the formulation of shape optimization is extended to include time-dependent loads and responses. A general objective functional is used to accommodate both structural shape optimization and passive control for mechanical problems. An adjoint sensitivity analysis is performed at the continuous level and subsequently discretized within the context of IGA. The methodology and its numerical implementation are tested using benchmark static problems of optimal shapes of orifices in plates under remote bi-axial tension and pure shear. Under quasi-static loading conditions, the method is validated using a passive control approach with an a priori known solution. Several applications of time-dependent mechanical problems are shown to illustrate the capabilities of this approach. In particular, a problem is considered where an external load is allowed to move along the surface of a structure. The shape of the structure is modified in order to control the time-dependent displacement of the point where the load is applied according to a pre-specified target. Copyright © 2015 John Wiley & Sons, Ltd.