Large deformations and stability in topology optimization

The present contribution focuses on the influence of geometrical nonlinearities on the structural behavior in the design process. The notion of the stiffest structure loses its clear definition in the case of nonlinear kinematics; here we will discuss this concept on the basis of different objectives. Apparently topology optimization is often a generator of slender struts, which tend to buckle before the structure is completely loaded. To include the instability phenomena into the design process, the critical load level will be determined directly; this condition will be included as an inequality constraint. Further on, to reduce the imperfection sensitivity, a geometrically modified structure including the imperfection shape is also introduced. The present optimization procedures are demonstrated by examples showing rather the principal effects of the enhancements than real practical design problems.     

Use of Optical Measuring Systems Based on Modern Electronic Tacheometers to Monitor Deformations of Surface Buildings and Structures

Theoretical bases are examined for the automation of geodetic measurements based on modern electronic tacheometers, and recommendations are given for their use.     

Arbitrary shaped deformations with DOGME

Published online: 5 February 2003     

Automatic expressive deformations for implying and stylizing motion

Three-dimensional computer animation often struggles to compete with the flexibility and expressiveness commonly found in traditional animation, particularly when rendered non-photorealistically. We present an animation tool that takes skeleton-driven 3D computer animations and generates expressive deformations to the character geometry. The technique is based upon the cartooning and animation concepts of “lines of action” and “lines of motion” and automatically infuses computer animations with some of the expressiveness displayed by traditional animation. Motion and pose-based expressive deformations are generated from the motion data and the character geometry is warped along each limb’s individual line of motion. The effect of this subtle, yet significant, warping is twofold: geometric inter-frame consistency is increased which helps create visually smoother animated sequences, and the warped geometry provides a novel solution to the problem of implied motion in non-photorealistic imagery. Object-space and image-space versions of the algorithm have been implemented and are presented.     

Advection approaches for single- and multi-material arbitrary Lagrangian–Eulerian finite element procedures

The essential feature in arbitrary Lagrangian–Eulerian (ALE) based finite element approaches is the additional requirement to consider flow effects of the materials and the solution variables through the computational domain. These flow effects are commonly known as advective effects. The present paper examines different advection strategies for the application of the ALE finite element method in a finite deformation solid mechanics framework, where especially micromechanical problems are referred to. The global solution algorithm is based on the well-known fractional step method that provides an operator splitting approach for the solution of the coupled ALE equations. Distinguishing the so-called single-material and the multi-material ALE method, different advection schemes based on volume- and material-associated advection procedures are required. For the latter case, the material interfaces are not resolved explicitly by the finite element mesh. Instead a volume-of-fluid interface tracking approach in terms of the volume fractions of the different material phases is applied.     

On the motion of mechanical networks

This paper develops the differential equations governing the motion of spatial networks to which mechanical features such as masses, stiffness coefficients, tensions and bending moments have been associated. These networks generalize the concept of particle systems introduced for the simulation of flexible bodies and extend their application to elastic models. The network deformation is shown to be related to the internal tensions and moments by a set of vectors, the directors of the network. A numerical example describing a rotating flexible beam is presented.     

Scalar-field-guided adaptive shape deformation and animation

In this paper, we propose a novel scalar-field-guided adaptive shape deformation (SFD) technique founded on PDE-based flow constraints and scalar fields of implicit functions. Scalar fields are used as embedding spaces. Upon deformation of the scalar field, a corresponding displacement/velocity field will be generated accordingly, which results in a shape deformation of the embedded object. In our system, the scalar field creation, sketching, and manipulation are both natural and intuitive. The embedded model is further enhanced with self-optimization capability. During the deformation we can also enforce various constraints on embedded models. In addition, this technique can be used to ease the animation design. Our experiments demonstrate that the new SFD technique is powerful, efficient, versatile, and intuitive for shape modeling and animation. This revised version was published online in February 2004 due to typesetting mistakes in the author correction process.     

Design sensitivity analysis in large deformation elasto‐plastic and elasto‐viscoplastic problems

Implicit time integration algorithm derived by Simo for his large‐deformation elasto‐plastic constitutive model is generalized, for the case of isotropy and associative flow rule, towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters. Combining it with the general formulation of design sensitivity analysis (DSA) for non‐linear finite element transient equilibrium problem, we come at a numerically efficient, closed‐form finite element formulation of DSA for large deformation elasto‐plastic and elasto‐viscoplastic problems, with various types of design variables (material constants, shape parameters). The paper handles several specific issues, like the use of a non‐algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change. Computational examples demonstrate abilities of the formulation and quality of results. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical analysis of partly wrinkled cylindrical inflated beams under bending and shear

This paper is aimed at assessing the nonlinear elastic response of an inflatable cylindrical beam through a simple mechanical model recently proposed by the authors for studying the equilibrium configurations of highly pressurised elastic membranes with general shapes. The attention is focused on beams loaded at mid-span with two different constraints, corresponding to simply-supported ends and built-in ends. The geometrical nonlinearities due to both the cross-sectional ovalization and wrinkling are carefully considered. In particular, the wrinkling of the membrane, clearly visible for load values much lower than the collapse load, is taken into account by means of an equivalent physical non-linearity. A two-states constitutive law for the material is assumed: when a fibre is stretched (the active state), its response is elastic, while when the fibre is contracted, no compressive force can be engendered in it (the passive state). The evolution of the cross-sectional ovalization, the size of the wrinkled regions and the magnitude of longitudinal and transverse stresses in the membrane are accurately determined for increasing levels of loads, up to collapse. The numerical results for the corresponding values of load and internal pressure, obtained through an expressly developed incremental-iterative algorithm, are compared with the experimental ones available in the literature.     

A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

A new algorithm is developed to improve the accuracy and efficiency of the material point method for problems involving extremely large tensile deformations and rotations. In the proposed procedure, particle domains are convected with the material motion more accurately than in the generalized interpolation material point method. This feature is crucial to eliminate instability in extension, which is a common shortcoming of most particle methods. Also, a novel alternative set of grid basis functions is proposed for efficiently calculating nodal force and consistent mass integrals on the grid. Specifically, by taking advantage of initially parallelogram‐shaped particle domains, and treating the deformation gradient as constant over the particle domain, the convected particle domain is a reshaped parallelogram in the deformed configuration. Accordingly, an alternative grid basis function over the particle domain is constructed by a standard 4‐node finite element interpolation on the parallelogram. Effectiveness of the proposed modifications is demonstrated using several large deformation solid mechanics problems. Copyright © 2011 John Wiley & Sons, Ltd.