A new paradigm coupling element-wise discrete-strain gaps with patch-wise reduced integration for efficient isogeometric nonlinear Kirchhoff–Love shell analysis
Toan Minh Le, H. Nguyen‐Xuan, Leonardo Leonetti
Abstract
This paper presents an effective and efficient approach, coupling the discrete-strain gap (DSG) method with the patch-wise reduced integration, to alleviate membrane-locking effects in quadratic NURBS-based isogeometric Kirchhoff–Love shell element, facilitating the nonlinear analysis of slender structures. Departing from the original DSG concept, we derive an element-wise DSG-based modification of membrane strains and then coherently spread the effects within the isogeometric analysis (IGA) framework, exploiting Bézier extraction. Specifically, the integral-form membrane strain gaps are first localized at the element level, and constructed in terms of the element’s compatible membrane strains. The corresponding discrete values are consequently obtained by evaluating the integrals at fixed typing points specified within the element parametric domain. Via a selectively reduced integration scheme, the target space required for accurately integrating the membrane-contributed energy terms is determined by the patch-wise reduced integration rule, accounting for the high continuity of the shape functions. The new approach results in a so-called C 1 - S 0 3 DSG element with the following merit features: effectively alleviating, if not eliminating, the membrane locking in both linear and nonlinear shell problems, significantly reducing computational costs through efficient numerical integration, preserving the nonzero-pattern and symmetry of stiffness relative to standard NURBS-based elements without introducing extra degrees of freedom. These advantages are intensively verified with various commonly used benchmarks, including linear elastic, buckling, large deformation , and large strain problems, confirming the superior performance and applicability of the proposed method.