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Tangent Stiffness (tangent + stiffness)

Distribution by Scientific Domains
Engineering80%

Terms modified by Tangent Stiffness

  • tangent stiffness matrix
    		•

    Selected Abstracts

    Operator-splitting method for real-time substructure testing

    EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2006
    Bin Wu
    Abstract It has been shown that the operator-splitting method (OSM) provides explicit and unconditionally stable solutions for quasi-static pseudo-dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real-time substructure testing (RST) when the velocity-dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward difference of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM-RST algorithm are investigated. It is shown that the OSM-RST is unconditionally stable so long as the non-linear stiffness and damping are of the softening type (i.e. the tangent stiffness and damping never exceed the initial values). The stability of the OSM-RST for structures with infinite tangent damping coefficient or stiffness is also proved, and the stability of the method for MDOF structures with a non-classical damping matrix is demonstrated by an energy criterion. The effects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM-RST is preserved when the experimental substructure generates velocity-dependent reaction forces, whereas the stability of real-time substructure tests based on the central difference method is worsened by the damping of the specimen. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    An embedded Dirichlet formulation for 3D continua

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010
    A. Gerstenberger
    Abstract This paper presents a new approach for imposing Dirichlet conditions weakly on non-fitting finite element meshes. Such conditions, also called embedded Dirichlet conditions, are typically, but not exclusively, encountered when prescribing Dirichlet conditions in the context of the eXtended finite element method (XFEM). The method's key idea is the use of an additional stress field as the constraining Lagrange multiplier function. The resulting mixed/hybrid formulation is applicable to 1D, 2D and 3D problems. The method does not require stabilization for the Lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level. Furthermore, only non-zero diagonal-terms are present in the tangent stiffness, which allows the straightforward application of state-of-the-art iterative solvers, like algebraic multigrid (AMG) techniques. Within this paper, the method is applied to the linear momentum equation of an elastic continuum and to the transient, incompressible Navier,Stokes equations. Steady and unsteady benchmark computations show excellent agreement with reference values. The general formulation presented in this paper can also be applied to other continuous field problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids.

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
    Part I: formulation, benchmarking
    Abstract This paper proposes a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra in 3D) in the large strain analysis of nearly incompressible solids. The new technique extends the F-bar method proposed by de Souza Neto et al. (Int. J. Solids and Struct. 1996; 33: 3277,3296) and is conceptually very simple: It relies on the enforcement of (near-) incompressibility over a patch of simplex elements (rather than the point-wise enforcement of conventional displacement-based finite elements). Within the framework of the F-bar method, this is achieved by assuming, for each element of a mesh, a modified (F-bar) deformation gradient whose volumetric component is defined as the volume change ratio of a pre-defined patch of elements. The resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near-incompressibility. As the original F-bar procedure, the present methodology preserves the displacement-based structure of the finite element equations as well as the strain-driven format of standard algorithms for numerical integration of path-dependent constitutive equations and can be used regardless of the constitutive model adopted. The new elements are implemented within an implicit quasi-static environment. In this context, a closed form expression for the exact tangent stiffness of the new elements is derived. This allows the use of the full Newton,Raphson scheme for equilibrium iterations. The performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two- and three-dimensional numerical examples. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Analysis of 3D problems using a new enhanced strain hexahedral element

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003
    P. M. A. Areias
    Abstract The now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell finite elements, is here explored in a versatile 3D low-order element which is identified as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including finite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent stiffness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several finite strain tests. Some examples involve finite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Functional tissue engineering for tendon repair: A multidisciplinary strategy using mesenchymal stem cells, bioscaffolds, and mechanical stimulation,

    JOURNAL OF ORTHOPAEDIC RESEARCH, Issue 1 2008
    David L. Butler
    Abstract Over the past 8 years, our group has been continuously improving tendon repair using a functional tissue engineering (FTE) paradigm. This paradigm was motivated by inconsistent clinical results after tendon repair and reconstruction, and the modest biomechanical improvements we observed after repair of rabbit central patellar tendon defects using mesenchymal stem cell-gel-suture constructs. Although possessing a significantly higher stiffness and failure force than for natural healing, these first generation constructs were quite weak compared to normal tendon. Fundamental to the new FTE paradigm was the need to determine in vivo forces to which the repair tissue might be exposed. We first recorded these force patterns in two normal tendon models and then compared these peak forces to those for repairs of central defects in the rabbit patellar tendon model (PT). Replacing the suture with end-posts in culture and lowering the mesenchymal stem cell (MSC) concentration of these constructs resulted in failure forces greater than peak in vivo forces that were measured for all the studied activities. Augmenting the gel with a type I collagen sponge further increased repair stiffness and maximum force, and resulted in the repair tangent stiffness matching normal stiffness up to peak in vivo forces. Mechanically stimulating these constructs in bioreactors further enhanced repair biomechanics compared to normal. We are now optimizing components of the mechanical signal that is delivered in culture to further improve construct and repair outcome. Our contributions in the area of tendon functional tissue engineering have the potential to create functional load-bearing repairs that will revolutionize surgical reconstruction after tendon and ligament injury. © 2007 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 26:1,9, 2008 [source]