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Geometric Non-linearity (geometric + non-linearity)

Distribution by Scientific Domains

Engineering	75%

Selected Abstracts

STRANDS: Interactive Simulation of Thin Solids using Cosserat Models

COMPUTER GRAPHICS FORUM, Issue 3 2002
Dinesh K. Pai
Strandsare thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, and vegetation in animation. Physical models based on spring meshes or 3D finite elements for such thin solids are either inaccurate or inefficient for interactive simulation. In this paper we show that models based on the Cosserat theory of elastic rods are very well suited for interactive simulation of these objects. The physical model reduces to a system of spatial ordinary differential equations that can be solved efficiently for typical boundary conditions. The model handles the important geometric non-linearity due to large changes in shape. We introduce Cosserat-type physical models, describe efficient numerical methods for interactive simulation of these models, and implementation results. [source]

A new triangular layered plate element for the non-linear analysis of reinforced concrete slabs

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2006
Y. X. Zhang
Abstract A new 3-node, 18-DOF triangular layered plate element is developed in this paper for the geometric and material non-linear analysis of isotropic plates and reinforced concrete slabs under service loads. The proposed model is a combination of Allman's 3-node, 9-DOF triangular membrane element with drilling degrees of freedom and the refined non-conforming 3-node, 9-DOF triangular plate-bending element RT9 in order to account for the coupling effects between membrane and bending actions. The element is modelled as a layered system of concrete and equivalent smeared steel reinforcement layers, and perfect bond is assumed between the concrete layers and the smeared steel layers. The maximum normal stress criterion is employed to detect cracking of the concrete, and a smeared fixed crack model is assumed. Both geometric non-linearity with large displacements but moderate rotations and material non-linearity, which incorporates tension, compression, concrete cracking and tension stiffening, are included in the model. An updated Lagrangian approach is employed as a solution strategy for the non-linear finite element analysis and a numerical example of reinforced concrete slab is given to demonstrate the efficacy of this robust element. Copyright © 2005 John Wiley & Sons, Ltd. [source]

On the design of energy,momentum integration schemes for arbitrary continuum formulations.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
Applications to classical, chaotic motion of shells
Abstract The construction of energy,momentum methods depends heavily on three kinds of non-linearities: (1) the geometric (non-linearity of the strain,displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric non-linearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law. Copyright © 2004 John Wiley & Sons, Ltd. [source]

c-Type method of unified CAMG and FEA.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2003
2D non-linear, 3D linear, Part 1: Beam, arch mega-elements
Abstract Computer-aided mesh generation (CAMG) dictated solely by the minimal key set of requirements of geometry, material, loading and support condition can produce ,mega-sized', arbitrary-shaped distorted elements. However, this may result in substantial cost saving and reduced bookkeeping for the subsequent finite element analysis (FEA) and reduced engineering manpower requirement for final quality assurance. A method, denoted as c-type, has been proposed by constructively defining a finite element space whereby the above hurdles may be overcome with a minimal number of hyper-sized elements. Bezier (and de Boor) control vectors are used as the generalized displacements and the Bernstein polynomials (and B-splines) as the elemental basis functions. A concomitant idea of coerced parametry and inter-element continuity on demand unifies modelling and finite element method. The c-type method may introduce additional control, namely, an inter-element continuity condition to the existing h-type and p-type methods. Adaptation of the c-type method to existing commercial and general-purpose computer programs based on a conventional displacement-based finite element method is straightforward. The c-type method with associated subdivision technique can be easily made into a hierarchic adaptive computer method with a suitable a posteriori error analysis. In this context, a summary of a geometrically exact non-linear formulation for the two-dimensional curved beams/arches is presented. Several beam problems ranging from truly three-dimensional tortuous linear curved beams to geometrically extremely non-linear two-dimensional arches are solved to establish numerical efficiency of the method. Incremental Lagrangian curvilinear formulation may be extended to overcome rotational singularity in 3D geometric non-linearity and to treat general material non-linearity. Copyright © 2003 John Wiley & Sons, Ltd. [source]