Analysis of hourglass instabilities and control in underintegrated finite element methods
From MaRDI portal
Publication:796361
DOI10.1016/0045-7825(84)90135-XzbMath0543.73104MaRDI QIDQ796361
J. Tinsley Oden, Olivier-Pierre Jacquotte
Publication date: 1984
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
stabilization matrixstabilization methodsspurious modeshourglass controla-posteriori stabilization methodhourglass instabilitiesunderintegrated stiffness matrix
Finite element methods applied to problems in solid mechanics (74S05) Numerical and other methods in solid mechanics (74S99)
Related Items
A modified representation of transverse shear in \(C^ 0\) quadrilateral plate elements ⋮ New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity ⋮ Numerical control of the hourglass instability ⋮ Dynamic strain localization in elasto-(visco-)plastic solids. II: Plane strain examples ⋮ A one-point integration quadrilateral with hourglass control in axisymmetric geometry ⋮ On the stabilization of the rectangular 4‐node quadrilateral element ⋮ Hourglass stabilization and the virtual element method ⋮ Numerical analysis of the direct method for 3D Maxwell's equation in Kerr-type nonlinear media ⋮ An efficient and rapid numerical quadrature to generate element matrices for quadrilateral and hexahedral elements in functionally graded materials (FGMs) ⋮ An essentially non-hourglass formulation for total Lagrangian smoothed particle hydrodynamics ⋮ Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems ⋮ A new finite element formulation for computational fluid dynamics: Development of an hourglass control operator for multidimensional advective-diffusive systems ⋮ The generation of element stiffness matrices from base matrices in the node space ⋮ A phenomenon of artificial odd-even grid oscillation and its presence in domain decomposition computation: algebraic analysis and numerical illustration ⋮ Global mode hourglassing control ⋮ An iterative technique for the finite element analysis of near-incompressible materials ⋮ A diffusion equation with hourglass control in an axisymmetric geometry ⋮ Finite element stabilization matrices - A unification approach ⋮ Mixed variational principles and stabilization of spurious modes in the 9-node element ⋮ Stabilization of the zero-energy modes of under-integrated isoparametric finite elements ⋮ A new numerical integration over arbitrary quadrilateral element based on smoothed strain energy and Richardson extrapolation ⋮ Unified and mixed formulation of the 8-node hexahedral elements by assumed strain method ⋮ A multiple-quadrature eight-mode hexahedral finite element for large deformation elastoplastic analysis ⋮ An accurate and efficient a posteriori control of hourglass instabilities in underintegrated linear and nonlinear elasticity ⋮ Finite element analysis of a class of problems in finite elastoplasticity based on the thermodynamical theory of materials of type N. ⋮ Stability, accuracy, and efficiency of some underintegrated methods in finite element computations
Cites Work
- A consistent control of spurious singular modes in the 9-node Lagrange element for the Laplace and Mindlin plate equations
- An accurate and efficient a posteriori control of hourglass instabilities in underintegrated linear and nonlinear elasticity
- Stability of some mixed finite element methods for Stokesian flows
- Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
- A stabilization matrix for the bilinear Mindlin plate element
- Penalty-finite element methods for the analysis of Stokesian flows
- Efficient linear and nonlinear heat conduction with a quadrilateral element
- A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
- Finite element methods for constrained problems in elasticity
- Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
