A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C¹ rational triangular Bézier spline discretizations

Abstract

Summary The analysis of the Kirchhoff plate is performed using rational Bézier triangles in isogeometric analysis coupled with a feature‐preserving automatic meshing algorithm. Isogeometric analysis employs the same basis function for geometric design as well as for numerical analysis. The proposed approach also features an automatic meshing algorithm that admits localized geometric features (eg, small geometric details and sharp corners) with high resolution. Moreover, the use of rational triangular Bézier splines for domain triangulation significantly increases the flexibility in discretizing spaces bounded by complicated nonuniform rational B‐spline curves. To raise the global continuity to C1 for the solution of the plate bending problem, Lagrange multipliers are leveraged to impose continuity constraints. The proposed approach also manipulates the control points at domain boundaries in such a way that the geometry is exactly described. A number of numerical examples consisting of static bending and free vibration analysis of thin plates bounded by complicated nonuniform rational B‐spline curves are used to demonstrate the advantage of the proposed approach.

On higher order parameters in cracked composite plates under far‐field pure shear

“…An evenly distributed shear stress of = 1 MPa is applied as tractions on remote boundaries of the plate, as shown in Figure 6A. 67,68 Normalized polar stress and strain components are extracted in a circular path of radius r∕a = 0.4 centred at the crack tip and then plotted against the crack tip angular position (see Figure 6B,C). The FE model consists of quadratic quadrilateral elements of type CPS8 with unit thickness and employs collapsed quarter-point elements at the crack tip.…”

“…Note that one may achieve a faster transition of element size from fine to coarse using a feature-preserving unstructured meshing tool proposed by Liu and Jeffers. 67,68 Normalized polar stress and strain components are extracted in a circular path of radius r∕a = 0.4 centred at the crack tip and then plotted against the crack tip angular position (see Figure 6B,C). The exact stress field is taken from (23).…”

A general degree semihybrid triangular compatible finite element formulation for Kirchhoff plates

“…Several triangular elements of this kind were proposed, whose main feature is to avoid the use of DOFs associated with nodal partial derivatives of order higher than one. Liu and Jeffers also proposed an isogeometric formulation wherein C 1 continuity is imposed using Lagrange multipliers on rational Bézier triangles. In terms of enforcement of C 1 continuity, their approach is similar to the one that we consider in Remark in Section 5.…”

Size-dependent thermo-mechanical free vibration analysis of functionally graded porous microbeams based on modified strain gradient theory

“…There also are researches focusing on analyzing microstructures using isogeometric analysis (IGA) in combination with different plate theories [90][91][92][93]. IGA has been successfully applied in several fields like: [94][95][96][97][98][99][100][101][102][103][104][105]. Ref.…”