Assumed strain stabilization of the eight node hexahedral element

doi:10.1016/0045-7825(93)90124-G

Computer Methods in Applied Mechanics and Engineering

Volume 105, Issue 2, June 1993, Pages 225-260

https://doi.org/10.1016/0045-7825(93)90124-G Get rights and content

Abstract

An accurate and robust stabilization based on the assumed strain method and an operator orthogonal to constant strain fields is presented for an eight-node hexahedral element with uniform reduced integration. The stabilization forces depend only on the element geometry and material properties. User specified parameters are not needed, yet the assumed strain stabilization is nearly as fast as perturbation type hourglass control in an explicit code. It has excellent coarse mesh accuracy for linear elastic bending, and is easily incorporated into a nonlinear program. The assumed strain field is also used with four-point integration which does not require stabilization. In addition, two forms of the B-matrix are studied and it is shown that the mean form is more efficient since it passes the patch test in a simplified form.

References (23)

T. Belytschko et al.
Hourglass control in linear and nonlinear problems
Comput. Methods Appl. Mech. Engng.
(1984)
T. Belytschko et al.
Efficient implementation of quadrilaterals with high coarse-mesh accuracy
Comput. Methods Appl. Mech. Engrg.
(1986)
T. Belytschko et al.
Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems
Comput. Methods Appl. Mech. Engrg.
(1991)
E.L. Wilson et al.
Incompatible displacement models
B.C. Koh et al.
New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity
Comput. Methods Appl. Mech. Engrg.
(1987)
J. Fish et al.
Elements with embedded localization zones for large deformation problems
Comput. & Structures
(1988)
J.O. Hallquist
UC1D-19401 Lawrence Livermore National Lab
D.P. Flanagan et al.
A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
Internat. J. Numer. Methods Engng.
(1981)
R.L. Taylor et al.
A nonconforming element for stress analysis
Internat. J. Numer. Methods Engrg.
(1976)
D. Kosloff et al.
Treatment of hourglass patterns in low and order finite element codes
Internat. J. Numer. Anal. Methods Geomech.
(1978)

W.K. Liu et al.

Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlineat continua

Comput. Methods Appl. Mech. Engrg.

(1988)

Cited by (227)

An implicit stabilized node-based smoothed finite element method for ultimate bearing capacity analysis of strip footing
2024, Engineering Analysis with Boundary Elements
The node-based smoothed finite element method (NS-FEM) has gained significant attention over the past decade. Nodal integration in NS-FEM, however, may lead to spurious oscillation of deformations of soil mass. To address the spurious oscillation of deformations associated with nodal integration, some stabilization techniques have been developed, but most of the stabilized NS-FEM have been implemented in the explicit finite element framework. The implicit framework, nonetheless, may offer some advantages including the high efficiency, good numerical accuracy, and suitability for handling large load increments and static problems. In this study, a novel stabilized NS-FEM by referring to the Taylor series expansion and incorporating the secant shear modulus, named sNS-FEM-KF(G_s), is developed in the implicit finite element framework. Based on the ultimate bearing capacity analysis of some strip footings, it is found that sNS-FEM-KF(G_s) may effectively eliminate the spurious oscillations observed in NS-FEM, and may resolve the overly-stiff behaviors of soil mass predicted by sNS-FEM-KF which is a reduced version of sNS-FEM-KF(G_s). Even compared to the standard finite element method with the 6-node triangular (T6) elements (i.e. FEM(T6)), sNS-FEM-KF(G_s) with linear 3-node triangular (T3) elements may outperform FEM(T6) in the investigated strip footing problems, indicating its good applicability in geotechnical analysis.
Low-velocity impact behavior of elliptic curved composite structures
2023, International Journal of Impact Engineering
Although many composite structures are inconsistently curved, such as the leading edges of aircraft wings, the variety of research in impact engineering is almost limited to the impact performance of plates or cylindrically curved specimens. It is not known whether the findings obtained from standardized tests can be transferred to curved structures or which adaptions are required. Therefore, a deeper understanding of the deformation and damage behavior of inconsistently curved structures is essential to transfer the observed impact behavior of flat specimens to general curved structures and therefore to utilize the full lightweight potential of a load-specific design. An accurate description of the procedure as well as the results of the experimental and numerical study of the low-velocity impact behavior of differently single-curved elliptic specimens is presented. To close the research gap of the impact behavior of geometries with curvatures between the plates and simplified leading edges, novel specimens geometries have been derived from established impact test standards. Glassfiber-reinforced specimens are subjected to an instrumented impact test at constant impact energy. This is numerically investigated by a stacked-layer model, which used cohesive zone modeling to enable the simulation of matrix cracking, fiber fracture and delamination. The resulting projected damage areas, as well as the force and deflection histories, were evaluated and section cuts were examined to discuss the damage morphology, formation and propagation process. Significant effects on maximum deflection, compliance and dynamic behavior on the size and morphology of damage were found.
Stabilized low-order finite-element formulation for static and dynamic simulation of saturated soils based on a hybrid integration scheme
2023, Computers and Geotechnics
This paper presents a stabilized linear finite-element formulation for three-dimensional (3D) elastoplastic static and dynamic coupled analyses of the soil skeleton and pore fluid. The proposed hybrid integration scheme can improve the speed and accuracy of the simulation while ensuring stability. The one-point reduced integration with hourglass stabilization and anti-locking strategy was used for the stress–strain calculation, while the full integration was adopted for analyzing other parts, such as the fluid phase. A robust pore-pressure stabilization method was derived to solve the oscillation problem for equal-order linear interpolation in the incompressible-undrained limit. In the field of large-scale 3D elastoplastic coupled solid–fluid simulations, academia has been committed to finding a method that considers the speed, stability, and accuracy of the simulation. The proposed finite-element formulation provides an effective solution for this purpose.
Impact responses of steel–concrete–steel sandwich panels with interlocked angle connectors: Experimental and numerical studies
2023, Thin-Walled Structures
This study explored the impact responses of a steel–concrete–steel sandwich composite panel with novel interlocked angle connectors (SCSP-IACs). Impact tests on nine SCSP-IACs were performed via a hemispherical hammer. The failure modes of all specimens were determined as the local punching failure of the concrete core. Moreover, the impact force–time and displacement–time histories and the permanent deformation were discussed. The experiment results showed that increasing the steel faceplate thickness and concrete core height enhanced the impact performance of the SCSP-IACs. By contrast, increasing the IAC spacing weakened the impact performance. Moreover, the interlocking bolts slightly affected the impact responses of the SCSP-IACs. A finite element (FE) model was established and verified with test data. The model was used to analyze the internal forces and energy absorption of the SCSP-IACs under impact loads. The internal force diagrams of the panels at different impact stages were provided, and a significant hogging moment was observed from the bending moment distributions. The FE results also showed that the zones close to the center of the panel absorbed most of the impact energy.
Finite element modelling of rolling dynamic compaction
2023, Computers and Geotechnics
Rolling dynamic compaction (RDC) utilises a heavy (6 to 12-tonne) non–circular module (impact roller) that pivots about its corners as it is towed, causing the module to fall to the ground and compact the underlying soil dynamically. This paper presents the development of a transient, non–linear finite element (FE) model of the Broons BH–1300 4–sided 8 tonne impact roller, undertaking multiple passes, using LS–DYNA, validated against a field trial and observations presented in the literature for the same coarse–grained material. The results of the numerical analyses demonstrate that the FE model provides reliable predictions of the 4-sided roller as observed in the field. Thus, the use of this FE model may provide high resolution insights into the capability of the impact roller, namely in predicting the settlement and densification of an underlying coarse-grained material. The FE model demonstrates significant soil improvement directly beneath the width of the roller to approximately 1.2 m depth. Residual improvement is shown to extend to approximately 2.5 m depth and 1.25 m laterally.
Second-order pyramid element formulations suitable for lumped-mass explicit methods in nonlinear solid mechanics
2023, Computer Methods in Applied Mechanics and Engineering
Pyramid elements can facilitate meshing by simplifying transitions from hexahedral to tetrahedral regions and a second-order basis promotes robust accuracy in unstructured meshes. Over the last decade, second-order C⁰ hexahedral, tetrahedral, and wedge elements that demonstrate important benefits have emerged for lumped-mass explicit dynamic methods in nonlinear solid mechanics. Whereas various second- and higher-order pyramid element formulations have been developed, none have addressed the necessities for lumped-mass explicit methods. Standard row-summation lumping for the popular 13- and 14-node pyramid elements, for example, produces negative lumped masses at the vertex nodes. Degeneration of hexahedral elements into pyramids is also unsatisfactory for second-order lumped-mass elements, except perhaps for low-interest fill regions. Such issues are resolved herein by developing 19-node second-order C⁰ pyramid element formulations that provide all-positive row-sum nodal lumped masses and are also compatible with the other suitable second-order lumped-mass elements. Other specific requirements of explicit methods are also addressed, and several uniform and selectively reduced pyramid quadrature rules are investigated. Application to a variety of benchmark problems demonstrates robust performance, including no apparent ill effects arising from using rational shape functions to treat the apex and good accuracy with pyramids placed in critical regions of highly nonlinear inelastic analyses.

View all citing articles on Scopus

View full text

Assumed strain stabilization of the eight node hexahedral element

Abstract

Comput. Methods Appl. Mech. Engng.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. & Structures

UC1D-19401 Lawrence Livermore National Lab

A uniform strain hexahedron and quadrilateral with orthogonal hourglass control

Internat. J. Numer. Methods Engng.

A nonconforming element for stress analysis

Internat. J. Numer. Methods Engrg.

Treatment of hourglass patterns in low and order finite element codes

Internat. J. Numer. Anal. Methods Geomech.

Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlineat continua

Comput. Methods Appl. Mech. Engrg.