This paper presents an eight‐node nonlinear solid‐shell element for static problems. The main goal of this work is to develop a solid‐shell formulation with improved membrane response compared with the previous solid‐shell element (MOS2013), presented in
- PAR ID:
- 10240681
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Volume:
- 108
- Issue:
- 11
- ISSN:
- 0029-5981
- Format(s):
- Medium: X Size: p. 1362-1380
- Size(s):
- p. 1362-1380
- Sponsoring Org:
- National Science Foundation
More Like this
-
Abstract Continuous‐assumed‐strain (CAS) elements were recently introduced (Casquero and Golestanian. Comput Methods Appl Mech Eng. 2022; 399:115354.) to remove the membrane locking present in quadratic ‐continuous NURBS‐based discretizations of linear plane curved Kirchhoff rods. In this work, we generalize CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane curved Timoshenko rods. CAS elements are an assumed strain treatment that interpolates the shear and membrane strains at the knots using linear Lagrange polynomials. Consequently, the inter‐element continuity of the shear and membrane strains is maintained. The numerical experiments considered in this work show that CAS elements excise the spurious oscillations in shear and membrane forces caused by shear and membrane locking. Furthermore, when using CAS elements with either full or reduced integration, the convergence of displacements, rotations, and stress resultants is independent of the slenderness ratio up to while the convergence is highly dependent on the slenderness ratio when using NURBS elements. We apply the locking treatment of CAS elements to quadratic ‐continuous NURBS and the resulting element type is named discontinuous‐assumed‐strain (DAS) elements. Comparisons among CAS and DAS elements show that once locking is properly removed, continuity across element boundaries results in higher accuracy than continuity across element boundaries. Lastly, CAS elements result in a simple numerical scheme that does not add any significant computational burden in comparison with the locking‐prone NURBS‐based discretization of the Galerkin method.more » « less
-
Abstract Soft materials are of major interest for biomechanics applications due to their high deformability and susceptibility to experience damage events under different loading scenarios. The present study is concerned with modelling damage evolution processes in these nonlinear materials whose structural responses are prone to locking when low-order kinematic interpolation is employed in the context of nonlinear Finite Element schemes. For this reason, a pair of gradient-enhanced continuum damage schemes are proposed with the aim of tackling mechanical failure problems in applications that exhibit shear and volumetric locking. In particular, we present the consistent formulation and the assessment of the corresponding performance of (i) a mixed displacement-enhanced assumed strain employing a total Lagrangian formulation, and (ii) a three-field mixed displacement-pressure-Jacobian formulation. The novel and formulations are consistently derived and numerically implemented, providing a satisfactory agreement with respect to built-in elements handling the treatment of shear and volumetric locking, respectively, in conjunction to the modelling damage phenomena via the use of a penalty-based gradient-enhanced formulation. This performance is examined via several numerical applications. Furthermore, the final example justifies the need for a formulation combining both mixed FE approaches to simulate problems encompassing both locking issues (shear and volumetric locking), which can be performed using a combination of the and herein proposed.
-
Abstract This work presents a hybrid shear‐flexible beam‐element, capable of capturing arbitrarily large inelastic displacements and rotations of planar frame structures with just one element per member. Following Reissner's geometrically exact theory, the finite element problem is herein formulated within nonlinear programming principles, where the total potential energy is treated as the objective function and the exact strain‐displacement relations are imposed as kinematic constraints. The approximation of integral expressions is conducted by an appropriate quadrature, and by introducing Lagrange multipliers, the Lagrangian of the minimization program is formed and solutions are sought based on the satisfaction of necessary optimality conditions. In addition to displacement degrees of freedom at the two element edge nodes, strain measures of the centroid act as unknown variables at the quadrature points, while only the curvature field is interpolated, to enforce compatibility throughout the element. Inelastic calculations are carried out by numerical integration of the material stress‐strain law at the cross‐section level. The locking‐free behavior of the element is presented and discussed, and its overall performance is demonstrated on a set of well‐known numerical examples. Results are compared with analytical solutions, where available, and outcomes based on flexibility‐based beam elements and quadrilateral elements, verifying the efficiency of the formulation.
-
Abstract Developing scientific literacy about water systems is critical for K‐12 students. However, even with opportunities to build knowledge about the hydrosphere in elementary classrooms, early learners may struggle to understand the water cycle (Forbes et al.,
; Gunckel et al., ; Zangori et al., ; Zangori et al., ). Scientific modeling affords opportunities for students to develop representations, make their ideas visible, and generate model‐based explanations for complex natural systems like the water cycle. This study describes a comprehensive evaluation of a 5‐year, design‐based research project focused on the development, implementation, revision, and testing of an enhanced, model‐centered version of the Full Option Science System (FOSS) Water (2005) unit in third grade classrooms. Here, we build upon our previous work (Forbes et al.,a; b; Vo et al., ; Zangori et al., ; Zangori et al., ) by conducting a comparative analysis of student outcomes in two sets of classrooms: (1) one implementing the modeling‐enhanced version of the FOSS Water unit developed by the research team ( n = 6), and 2) another using the standard, unmodified version of the same curricular unit (n = 5). Results demonstrate that teachers in both conditions implemented the two versions of the curriculum with relative fidelity. On average, students exposed to the modeling‐enhanced version of the curriculum showed greater gains in their model‐based explanations for the hydrosphere. Engagement in scientific modeling allowed students to articulate hydrologic phenomena by (1) identifying various elements that constitute the hydrosphere, (2) describing how these elements influenced the movement of water in the hydrosphere, and (3) demonstrating underlying processes that govern the movement of water in the hydrosphere. -
Abstract There are several models of the use of geometric and feature cues in reorientation (Cheng, Huttenlocher, & Newcombe,
). The adaptive combination approach posits that people integrate cues with weights that depend on cue salience and learning, or, when discrepancies are large, they choose between cues based on these variables (Cheng, Shettleworth, Huttenlocher, & Rieser, ; Newcombe & Huttenlocher, ). In a new paradigm designed to evaluate integration and choice, disoriented participants attempted to return to a heading direction, in a trapezoidal enclosure in which feature and geometric cues both unambiguously specified a heading, but later the feature was moved. With discrepancies greater than 90 degrees, participants choose geometry. With smaller discrepancies, integration appeared in three of five situations; otherwise, participants used geometry alone. Variation depended on direction of feature movement and whether the nearest corner was acute or obtuse. The results have implications for contrasting adaptive combination and modularity theory, and for future research, offering a new paradigm for reorientation research, and for testing cue integration more broadly.