Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications

Optimal design methods that use continuum mechanics models are capable of generating suitable topology, shape, and dimensions of compliant mechanisms for desired specifications. Synthesis procedures that use linear elastic finite element models are not quantitatively accurate for large displacement situations. Also, design specifications involving nonlinear force-deflection characteristics and generation of a curved path for the output port cannot be realized with linear models. In this paper, the synthesis of compliant mechanisms is performed using geometrically nonlinear finite element models that appropriately account for large displacements. Frame elements are chosen because of ease of implementation of the general approach and their ability to capture bending deformations. A method for nonlinear design sensitivity analysis is described. Examples are included to illustrate the usefulness of the synthesis method.

Download Full-text

Towards the Design of Compliant Continuum Topologies With Geometric Nonlinearity

Volume 1: 25th Design Automation Conference ◽

10.1115/detc99/dac-8578 ◽

1999 ◽

Author(s):

A. Saxena ◽

G. K. Ananthasuresh

Keyword(s):

Finite Element ◽

Linear Models ◽

Compliant Mechanisms ◽

Synthesis Method ◽

Finite Element Models ◽

Computationally Efficient ◽

Mechanics Model ◽

Nonlinear Design ◽

Nonlinear Force ◽

Synthesis Procedure

Abstract Optimal design methods that use continuum mechanics model for the deformation of the elastic body, are capable of generating suitable topology, shape, and dimensions of compliant mechanisms for desired specifications. Elastic analysis with linear finite element models employed in the synthesis procedures to date is not quantitatively accurate for large displacement situations. Also, the design specifications involving nonlinear force-deflection characteristics and generation of a curved path for the output port are difficult to realize with linear models. In this paper, the synthesis of compliant mechanisms is performed using geometrically nonlinear finite element models that appropriately account for large displacements. Frame elements are chosen for developing the synthesis procedure because of ease of implementation of the general approach and their ability to capture bending deformations. A computationally efficient method for computing the nonlinear design sensitivities is described. Examples are included to illustrate the usefulness of the synthesis method.

Download Full-text

COMPARATIVE ANALYSIS OF THE PARAMETERS OF FINITE-ELEMENT MODELS OF SOILS OBTAINED BY NUMERICAL METHODS

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY ◽

10.24143/1812-9498-2017-1-23-31 ◽

2017 ◽

pp. 23-31

Author(s):

Vladimir Ivanovich Matselya ◽

Igor Nikolaevich Seelev ◽

Alexey Valentinovich Lekontsev ◽

Robert Rafaelevich Khafizov ◽

Pavel Viktorovich Yakovlev ◽

...

Keyword(s):

Finite Element ◽

Comparative Analysis ◽

Numerical Methods ◽

Small Deformation ◽

Finite Element Models ◽

Linear Elastic ◽

Industrial Buildings ◽

Test Models ◽

Weak Points ◽

Plaxis 3D

The popularity of numerical methods for modeling soil bases determines the increased demand for the accuracy of calculations. The choice of a model that meets the requirements of accuracy of calculations and minimization of costs is determined by comparative analysis of common soil models described in scientific literature and used in calculations of sediments and dynamic effects of buildings (finite element linear elastic, elastic, ideal-plastic, Mora - Coulomb with strengthening, elasto-plastic with strengthening at small deformation). The results have been obtained on test models using finite element method in the environment of PLAXIS 3D and SCAD Office programs. In order to compare results obtained, subject to requirements of the current regulatory documents, a comparative analysis of soils was carried out according to the model of Body of rules 22.13330.2011 "Foundations of buildings and structures". The analysis results were used for choosing an optimal model of soil bases of industrial buildings estimated in earthquake-proof design. It should be noted that the strong and weak points identified for each model justify the choice of the best model for each particular case.

Download Full-text

Development and Comparison of Laplace Domain Models for Non-Slender Beams and Application to a Half-Car Model With Flexible Body

Volume 2: Dynamics, Vibration and Control; Energy; Fluids Engineering; Micro and Nano Manufacturing ◽

10.1115/esda2014-20348 ◽

2014 ◽

Author(s):

R. Michael Van Auken

Keyword(s):

Finite Element ◽

Rotary Inertia ◽

Flexible Body ◽

Finite Element Models ◽

Laplace Domain ◽

Linear Elastic ◽

Area Of Interest ◽

Slender Beams ◽

Domain Models ◽

Shear Effects

Math models of flexible dynamic systems have been the subject of research and development for many years. One area of interest is exact Laplace domain solutions to the differential equations that describe the linear elastic deformation of idealized structures. These solutions can be compared to and complement finite order models such as state-space and finite element models. Halevi (2005) presented a Laplace domain solution for a finite length rod in torsion governed by a second order wave equation. Using similar methods Van Auken (2010, 2012) presented a Laplace domain solution for the transverse bending of an undamped uniform slender beam based on the fourth order Euler-Bernoulli equation, where it was assumed that rotary inertia and shear effects were negligible. This paper presents a new exact Laplace domain solution to the Timoshenko model for an undamped uniform non-slender beam that accounts for rotary inertia and shear effects. Example models based on the exact Laplace domain solution are compared to finite element models and to slender beam models in order to illustrate the agreement and differences between the methods and models. The method is then applied to an example model a half-car with a flexible body.

Download Full-text

Real Time Techniques for Nonlinear Tissue Deformation in Surgical Simulation

ASME 2007 Summer Bioengineering Conference ◽

10.1115/sbc2007-172518 ◽

2007 ◽

Author(s):

Suvranu De ◽

Yi-Je Lim

Keyword(s):

Finite Element ◽

Real Time ◽

Surgical Simulation ◽

Computational Technique ◽

Finite Element Models ◽

Geometrically Nonlinear ◽

Time Performance ◽

Surgical Tool ◽

Surgical Simulations ◽

Tissue Deformations

The requirement of real time performance, crucial to multimodal surgical simulations, imposes severe demands in terms of computational efficiency. A physics-based meshfree computational technique known as the Point-Associated Finite Field (PAFF) approach has been developed to circumvent many outstanding problems associated with traditional mesh-based computational schemes and has been applied in this paper to the modeling of geometrically nonlinear tissue deformations. The technique is based on a novel combination of multiresolution approach coupled with a fast reanalysis scheme in which the response predicted by an underlying linear PAFF model is enhanced in the local neighborhood of the surgical tool-tip by a nonlinear model. We present performance comparisons of PAFF with traditional finite element models.

Download Full-text

Tuning finite element models using design sensitivity

10.2514/6.1999-1454 ◽

1999 ◽

Author(s):

Paul Blelloch ◽

James Freymiller

Keyword(s):

Finite Element ◽

Design Sensitivity ◽

Finite Element Models

Download Full-text

A Finite Element Geometrically Nonlinear Dynamic Formulation of Flexible Multibody Systems Using a New Displacements Representation

Journal of Vibration and Acoustics ◽

10.1115/1.2889764 ◽

1997 ◽

Vol 119 (4) ◽

pp. 573-581 ◽

Cited By ~ 19

Author(s):

J. Mayo ◽

J. Domi´nguez

Keyword(s):

Finite Element ◽

Multibody Systems ◽

Strain Energy ◽

Degrees Of Freedom ◽

Synthesis Method ◽

Geometrically Nonlinear ◽

Motion Equations ◽

Constant Stiffness ◽

Elastic Nonlinearity ◽

External Forces

In previous work (Mayo, 1993), the authors developed two geometrically nonlinear formulations of beams inflexible multibody systems. One, like most related methods, includes geometric elastic nonlinearity in the motion equations via the stiffness terms (Mayo and Domi´nguez, 1995), but preserving terms, in the expression for the strain energy, of a higher-order than most available formulations. The other formulation relies on distinguishing the contribution of the foreshortening effect from that of strain in modelling the displacement of a point. While including exactly the same nonlinear terms in the expression for the strain energy, the stiffness terms in the motion equations generated by this formulation are exclusively limited to the constant stiffness matrix for the linear analysis because the terms arising from geometric elastic nonlinearity are moved from elastic forces to inertial, reactive and external forces, which are originally nonlinear. This formulation was reported in a previous paper (Mayo et al, 1995) and used in conjunction with the assumed-modes method. The aim of the present work is to implement this second formulation on the basis of the finite-element method. If, in addition, the component mode synthesis method is applied to reduce the number of degrees of freedom, the proposed formulation takes account of the effect of geometric elastic nonlinearity on the transverse displacements occurring during bending without the need to include any axial vibration modes. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms.

Download Full-text