An Insight on NURBS Based Isogeometric Analysis, Its Current Status and Involvement in Mechanical Applications

We present an open Octave/Matlab package nligaStruct, for linear and nonlinear isogeometric analysis of thin-walled structures. nligaStruct is an extension of NLIGA in aspect of isogeometric structural analysis. A framework for Bézier extraction of T-spline and NURBS is embedded in the simulation pipeline. Both Reissner–Mindlin and Kirchhoff–Love assumptions are considered in the case of static bending and free vibration analysis of thin-walled structures (plates and shells). The convergence behaviors of these two assumptions for both plate and shell are thoroughly studied and compared. The discrete formulations for large deformation of Kirchhoff–Love shells considering geometrical and material nonlinearity are detailedly derived and carefully implemented. Three types of hyperelastic materials, including St. Venant–Kirchhoff, incompressible neo-Hookean and compressible neo-Hookean, are employed in the large deformation of Kirchhoff–Love shells. A series of popular benchmark examples and their geometrical models are demonstrated in the package. The numerical results are validated by comparing with analytical solutions and that obtained from commercial software. The postprocessing is self-contained and implemented by tessellation of Bézier elements. Finally, complete source codes and the data obtained from numerical examples are fully provided and free to access. 

Numerical implementation for isogeometric analysis of thin-walled structures based on a Bézier extraction framework: nligaStruct

Adaptive extended isogeometric upper-bound limit analysis of cracked structures

Large deformation frictional contact formulations for isogeometric Kirchhoff–Love shell

This paper develops a multi-patch isogeometric Kirchhoff–Love shell method for post-buckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical, spherical, and conoidal shell structures, which are built with single or multiple NURBS patches. A penalty strategy is employed to weakly couple nonconforming interfaces between adjacent patches. The coupling work induced by enforcing displacement continuity and rotational continuity is added to the equilibrium equation, and the corresponding stiffness matrix is derived in detail. A simplified arc-length method is utilized to capture the complex equilibrium paths including snap-through and snap-back behaviors. Five distribution patterns of the shells including uniform (UD), V-type, A-type, O-type, and X-type are considered. The cylindrical and spherical shells are subjected to concentrated loadings at central points while for conoidal shells the concentrated loadings are enforced at the center points of an edge. The post-buckling of isotropic and laminated shell structures is first studied to validate the developed formulations by comparing the obtained results with those given in existing literature. Then a series of numerical examples considering nonlinear FG-GPLRC shell problems are conducted to explore the effect of various parameters like geometric dimensions, GPL distribution patterns, and shell thickness on the mechanical performance. Finally, the post-buckling of a cylindrical shell subjected to an offset concentrated load, with extremely complicated equilibrium paths, is modeled and analyzed by using the developed multi-patch isogeometric method. The numerical results reveal that the X-type GPL distribution pattern demonstrates better performance in load–deflection responses and provides the largest buckling critical load among the five patterns. Additionally, the increase in height ratio could deteriorate the stability performance of FG-GPLRC conoidal shells. 

Multi-patch isogeometric Kirchhoff–Love shell analysis for post-buckling of functionally graded graphene platelets reinforced composite shells

NLIGA: A MATLAB framework for nonlinear isogeometric analysis

https://www.techscience.com/CMES/v123n2/38701/pdf

T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems

School of Mechanical Engineering and Automation, Beihang University, Beijing, PR China, Beijing Engineering Technological Research Center of High-E cient & Green CNC Machining Process, Beijing, PR China, Beihang University, duxiaoxiao@buaa.edu.cn Beihang University, zhaog@buaa.edu.cn Beihang University, jrrt@buaa.edu.cn Beihang University, windowsgmy@126.com Beihang University, feliciamail@buaa.edu.cn Beihang University, williamyjm@163.com

/pdf/triangular-and-quadrilateral-bezier-discretizations-of-3u5qo2fsvp.pdf

Triangular and Quadrilateral Bezier Discretizations of Trimmed CAD Surfaces and Its Application to the Isogeometric Analysis

School of Mechanical Engineering and Automation, Beihang University, Beijing, PR China, Beijing Engineering Technological Research Center of High-E cient & Green CNC Machining Process, Beijing, PR China, Beihang University, feliciamail@buaa.edu.cn Beihang University, zhaog@buaa.edu.cn Beihang University, jrrt@buaa.edu.cn Beihang University, duxiaoxiao@buaa.edu.cn Beihang University, windowsgmy@126.com

/pdf/nurbs-based-isogeometric-analysis-for-small-deformation-of-27mpsm60r1.pdf

NURBS-based Isogeometric Analysis for Small Deformation of Viscoplastic and Creep Problems

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Papers

NLIGA: A MATLAB framework for nonlinear isogeometric analysis

T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems

Triangular and Quadrilateral Bezier Discretizations of Trimmed CAD Surfaces and Its Application to the Isogeometric Analysis

NURBS-based Isogeometric Analysis for Small Deformation of Viscoplastic and Creep Problems