Showing papers on "Direct stiffness method published in 2010"

Optimization of Variable-Stiffness Panels for Maximum Buckling Load Using Lamination Parameters

Abstract: With the large-scale adoption of advanced fiber placement technology in industry, it has become possible to fully exploit the anisotropy of composite materials through the use of fiber steering. By steering the composite fibers in curvilinear paths, spatial variation of stiffness can be induced resulting in beneficial load and stiffness distribution patterns. One especially relevant area in which fiber steering has proved its effectiveness is in improving buckling loads of composite panels. Previous research used predefined forms of fiber angle variations and the coefficients of these analytic expressions were used as design variables. Alternatively, the local ply angles were used as design variables directly. In this paper, a framework is developed to treat the most general approach that considers the largest possible design space. The use of lamination parameters efficiently defines stiffness variation over a structural domain with the minimum number of variables. A conservative reciprocal approximation scheme is introduced. The inverse buckling factor is expanded linearly in terms of the in-plane stiffness and in terms of the inverse bending stiffness. The new approximation scheme is convex in lamination parameter space. Numerical results demonstrate improvements in excess of 100% in buckling loads of variable-stiffness panels compared to the optimum constant stiffness designs. Buckling load improvements are attributed primarily to in-plane load redistribution, which is confirmed both by the prebuckling stress distribution as well as by comparing the performance of designs optimized with variation of both in-plane and bending stiffness to those optimized with only bending stiffness variation. A tradeoff study between in-plane stiffness and buckling performance is also presented and shows the benefits of variable-stiffness design in enlarging the design possibilities of composite panels.

Dimensional Optimization Design of the Four-Cable-Driven Parallel Manipulator in FAST

Abstract: For the design of the five-hundred-meter aperture spherical radio telescope (FAST), a four-cable-driven parallel manipulator, which is long in span and heavy in weight, is adopted as the first-level adjustable feed-support system. The purpose of this paper is to optimize dimensions of the four-cable-driven parallel manipulator to meet the workspace requirement of constraint condition in terms of cable tension and stiffness. Accordingly, this optimization method adopts catenary simplification in order to set up the cable tension equilibrium equations, preliminarily optimizing three important dimensional parameters. Stiffness of the cable is also taken into consideration because of its effect on work performance of a cable-driven parallel manipulator. However, the stiffness value of a cable-driven parallel manipulator is not totally credible by traditional theoretical analysis. Therefore, an experimental method for stiffness analysis is presented in this paper. It applies Buckingham π theorem to set up an experimental stiffness similarity model to obtain a more credible stiffness value, which is used in the optimization process. In this way, dimensional optimization is realized with a set of optimized dimensions for building the feed-support system in the FAST. More importantly, the stiffness similarity model can be universally adopted in stiffness analysis of other large cable-driven parallel manipulator.

A vehicle–bridge linear interaction model and its validation

Abstract: A linear wheel–rail interaction model for the vehicle–bridge coupling system is presented in this paper. The vehicle subsystem is modeled by the rigid-body dynamics method, the bridge subsystem by both the direct stiffness method and superposition method, and the wheel–rail interaction by the "corresponding assumption" and simplified Kalker creep theory. Based on the above modeling for the wheel–rail interaction system, linear simultaneous equations are established and solved. As a case study, the response of the Pioneer train traversing a 24 m simply–supported girder bridge is calculated. The proposed analysis procedure is validated through comparison of the calculated results with the measured ones. Also, some vibration characteristics of the system are discussed.

Stiffness of Reinforced Concrete Frame Members for Seismic Analysis

Abstract: Effective stiffness assumption in the modeling of reinforced concrete (RC) frame members is important for seismic design because it directly affects the building periods and dynamic response, particularly deflection and internal force distribution. Different opinions about the magnitude and governing parameters of effective stiffness persist in different national codes and literature. In this paper, parameters governing the effective stiffness of RC frame members are identified and their relative influence is determined using the three-component approach. Based on parametric study, lower-bound and upper-bound estimates of effective stiffness for the normal range of parameters in RC frame buildings are obtained and verified with experimental results. Various effective stiffness relationships and equations available in literature are also compared. Separate models for the effective stiffness of normal-strength and high-strength concrete members are proposed. The models can be used for the design of buildings without excessive computational effort.

Dynamic stiffness matrix of an axially loaded slenderdouble-beam element

Abstract: The dynamic stiffness matrix is formulated for an axially loaded slender double-beam element in which both beams are homogeneous, prismatic and of the same length by directly solving the governing differential equations of motion of the double-beam element. The Bernoulli-Euler beam theory is used to define the dynamic behaviors of the beams and the effects of the mass of springs and axial force are taken into account in the formulation. The dynamic stiffness method is used for calculation of the exact natural frequencies and mode shapes of the double-beam systems. Numerical results are given for a particular example of axially loaded double-beam system under a variety of boundary conditions, and the exact numerical solutions are shown for the natural frequencies and normal mode shapes. The effects of the axial force and boundary conditions are extensively discussed.

Two-dimensional rod theory for approximate analysis ofbuilding structures

Abstract: It has been known that one-dimensional rod theory is very effective as a simplified analytical approach to large scale or complicated structures such as high-rise buildings, in preliminary design stages. It replaces an original structure by a one-dimensional rod which has an equivalent stiffness in terms of global properties. If the structure is composed of distinct constituents of different stiffness such as coupled walls with opening, structural behavior is significantly governed by the local variation of stiffness. This paper proposes an extended version of the rod theory which accounts for the two-dimensional local variation of structural stiffness; viz, variation in the transverse direction as well as longitudinal stiffness distribution. The governing equation for the two-dimensional rod theory is formulated from Hamilton`s principle by making use of a displacement function which satisfies continuity conditions across the boundary between the distinct structural components in the transverse direction. Validity of the proposed theory is confirmed by comparison with numerical results of computational tools in the cases of static, free vibration and forced vibration problems for various structures.

A new mechanical structure for adjustable stiffness devices with lightweight and small size

Abstract: In this paper, we propose a new mechanical structure for adjustable stiffness devices with lightweight and small size. The proposed structure utilize a ball screw mechanism to adjust a relationship between infinitesimal displacements of joint rotation and a linear spring. Then, stiffness around the joint is adjusted. Unlike many of other adjustable stiffness structures, available elastic energy of the elastic element is maximum when the stiffness of the proposed structure is maximum. Therefore, the elastic element of this structure can be smaller and more lightweight than the other structures. Another advantage of the proposed structure is to require fewer and smaller mechanical parts, because the proposed mechanism mostly requires the ball screw mechanism and the linear spring. We developed an actual hardware to test the proposed structure.

Direct versus iterative model updating methods for mass and stiffness matrices

Abstract: A comparative study is performed for the direct and iterative methods for updating the structural matrices based on measured data. The former was derived from the orthogonality constraints by replacing the modal vector of concern by the modal matrix in computing the correction matrices. 1 The iterative method used is the improved inverse eigensenstivity method. 2 Through the numerical studies, it was demonstrated that both methods yield good results. However, the direct updating method is found to be more suitable for engineering applications due to its ease in treating multi-modes and higher efficiency, especially for complicated structures.

Introduction to Finite Element Analysis Using SolidWorks Simulation 2010

Abstract: The primary goal of Introduction to Finite Element Analysis Using SolidWorks Simulation is to introduce the aspects of Finite Element Analysis (FEA) that are important to engineers and designers. Theoretical aspects of Finite Element Analysis are also introduced as they are needed to help better understand the operation. The primary emphasis of the text is placed on the practical concepts and procedures needed to use SolidWorks Simulation in performing Linear Static Stress Analysis and basic Model Analysis. This text covers SolidWorks Simulation and the lessons proceed in a pedagogical fashion to guide you from constructing basic truss elements to generating three-dimensional solid elements from solid models. This text takes a hands-on, exercise-intensive approach to all the important Finite Element Analysis techniques and concepts. This textbook contains a series of thirteen tutorial style lessons designed to introduce beginning FEA users to SolidWorks Simulation. The basic premise of this book is that the more designs you create using SolidWorks Simulation, the better you learn the software. With this in mind, each lesson introduces a new set of commands and concepts, building on previous lessons. Table of Contents Introduction 1. The Direct Stiffness Method 2. Truss Elements in Two-Dimensional Spaces 3. 2D Trusses in MS Excel and the Truss Solver 4. Truss Elements in SolidWorks Simulation 5. SolidWorks Simulation Two-Dimensional Truss Analysis 6. Three-Dimensional Truss Analysis 7. Basic Beam Analysis 8. Beam Analysis Tools 9. Statically Indeterminate Structures 10. Two-Dimensional Surface Analysis 11. Three-Dimensional Solid Elements 12. Three-Dimensional Thin Shell Analysis 13. Dynamic Model Analysis Index

Stiffness modeling of a family of 6-DoF parallel mechanisms with three limbs based on screw theory

Abstract: The stiffness modeling of a family of six degrees of freedom (DoF) parallel mechanisms with configurations of 3-RUPU is presented The mobility of the mechanisms is firstly analyzed, and then the stiffness analysis and modeling of the family of mechanisms is developed by a novel screw-theory based method The method employs screw theory as a tool for force analysis and deformation analysis Based on the developed stiffness model, two global flexibility indices, which refer to the maximum and minimum singular values of compliance matrix, are introduced to evaluate the compliance of parallel mechanisms Finally, a case study is presented to demonstrate the effectiveness of the method in analyzing and evaluating the stiffness behavior of the presented parallel mechanisms

Stiffness Analysis of a Spatial Parallel Mechanism With Flexible Moving Platform

Abstract: In this paper, stiffness analysis of a 3-DOF spatial, 3-PSP type, parallel manipulator is investigated. Most previous stiffness analysis studies of parallel manipulators are performed using lumped model as well as assuming a rigid moving platform. In this paper, unlike traditional stiffness analysis, the moving platform is assumed to be flexible. Additionally, a continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano’s theorem [1]. For this purpose, first we solve inverse kinematics problem then We must find relationship between the applied external torques on the moving platform and the resultant joints forces. Next, strain energy moving platform is calculated. Strain energy of this element is calculated using force analysis and inverse kinematics problem. Finally, a FEM model is generated and used to simulate the physical structure. Simulation results are compared with the analytical model.Copyright © 2010 by ASME

Finite Element Analysis of Plate on Layered Tensionless Foundation

Abstract: The method of calculations of a thick plate on the two-parameter layered foundation by the finite element method is presented. The numerical model allows to add a few (number of) foundation layers. The expressions for the element stiffness matrices of the foundation are based on 18-node zero-thickness interface elements. For modelling of thick plates the 9-node Mindlin element of the Lagrange family is used. The formulation of the problem takes into account the shear deformation of the plate and unilateral contact conditions between plate and foundation. The tensionless character of the foundation is achieved by removing from the global stiffness matrix the appropriate part of foundation stiffness attached to the node being in the separation stage. The advantages of the proposed algorithm are illustrated by numerical examples.

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

Abstract: In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

Compound stiffness modelling of an integrated open-die forging centre with serial–parallel heavy-duty manipulators:

Abstract: This paper presents a method for modelling the compound stiffness of an integrated open-die forging centre that consists of a forging press as well as a manipulator that handles the workpiece. Open-die forging has considerable differences to general machining processes due to the complex plastic deformation effects created by consecutive forging strikes. The manipulator must comply with the movement of the workpiece during forging. The stiffness of the integrated system mainly comes from two sources: the compliance of the manipulator and the elastic deformation of the workpiece during forging. First, the stiffness matrix of the workpiece is derived using the theory of mechanics of materials. Then, the complete Cartesian stiffness matrix of the manipulator is developed by using the conservative congruence transformation method. Finally, the compound stiffness model is constructed by combining these two stiffness matrices. A numerical algorithm is developed that is able to simulate the compliance mo...

Structural topology optimization considering correlated uncertainties in elastic modulus

Abstract: An existing perturbation-based method is extended to consider correlated uncertainties in structural topology optimization problems. The proposed method uses perturbation technique to model uncertainties in the geometry of structures and material properties, and transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. This leads to significant computational savings when compared with Monte Carlo-based optimization, which involve multiple formations and inversions of the global stiffness matrix. We study two numerical examples to show the importance of correlation in uncertainty modeling and to verify the proposed method. Numerical examples show that results obtained from the proposed method are in excellent agreement with those obtained when using Monte Carlo-based optimization.

Design and Analysis of a Variable Stiffness Mechanism

Abstract: The design and analysis of a mechanism with variable stiffness is examined. The mechanism, which is a simple arrangement of two springs, a lever arm and a pivot bar, has an effective stiffness that is a rational function of the horizontal position d of the pivot. The external pure force acting on the system is constrained to always remain vertical. The effective stiffness is varied by changing d while keeping the point of application of the external load constant. The expression for the effective stiffness is derived. A reverse analysis is also carried out on the mechanism. Special design cases are considered. The dynamic equation of the system is derived and used to deduce the natural frequency of the mechanism from which some insights were gained on the dynamic behavior of the mechanism.Copyright © 2010 by ASME

Design and modeling of variable stiffness joints based on compliant flexures

Abstract: The development of safe and dependable robots for physical human-robot interaction is actually changing the way robot are designed introducing several new technological issues. Outstanding examples are the adoption of soft covers and compliant transmissions or the definition of motion control laws that allow a compliant behavior in reaction to possible collisions, while preserving accuracy and performance during the motion in the free space. In this scenario, a growing interest is devoted to the study of variable stiffness joints. With the aim of improving the compactness and the flexibility of existing mechanical solutions, a variable stiffness joint based on the use of compliant flexures is investigated. The proposed concept allows the implementation of a desired stiffness profile and range along with the selection of the maximum joint deflection. In particular, this paper reports a systematic procedure for the synthesis of a fully-compliant mechanism used as a non-linear transmission, together with a preliminary design of the overall joint.Copyright © 2010 by ASME

On Cartesian stiffness matrices in rigid body dynamics: an energetic perspective

Abstract: Several Cartesian stiffness matrices for a single rigid body subject to a conservative force field are developed in this paper The treatment is based on energetic arguments and an Euler angle parameterization of the rotation of the rigid body is employed Several new representations for the stiffness matrix are obtained and the relation to other works on Cartesian stiffness matrices and Hessians is illuminated Additional details are presented with respect to determining the Cartesian stiffness matrix for a pair of rigid bodies, as well as for a system of rigid bodies constrained to a plane