Derivatives of Buckling Loads and Vibration Frequencies With Respect to Stiffness and Initial Strain Parameters

1990 ◽  
Vol 57 (1) ◽  
pp. 18-24 ◽  
Author(s):  
Raphael T. Haftka ◽  
Gerald A. Cohen ◽  
Zenon Mro´z
Keyword(s):  
Virtual Work ◽  
Direct Method ◽  
General Purpose ◽  
Initial Strain ◽  
Nonlinear Structures ◽  
Vibration Frequencies ◽  
Finite Element Program ◽  
Buckling Loads ◽  
Element Program ◽  
Derivatives Of

A uniform variational approach to sensitivity analysis of vibration frequencies and bifurcation loads of nonlinear structures is developed. Two methods of calculating the sensitivities of bifurcation buckling loads and vibration frequencies of nonlinear structures, with respect to stiffness and initial strain parameters, are presented. A direct method requires calculation of derivatives of the prebuckling state with respect to these parameters. An adjoint method bypasses the need for these derivatives by using instead the strain field associated with the second-order post-buckling state. An operator notation is used and the derivation is based on the principle of virtual work. The derivative computations are easily implemented in structural analysis programs. This is demonstrated by examples using a general purpose, finite element program and a shell-of-revolution program.

Unit Load Method for Deflections of Planar, Nonlinear Structures

1980 ◽  
Vol 102 (4) ◽  
pp. 781-786 ◽  
Author(s):  
G. Szuladzinski
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Nonlinear Material ◽  
Nonlinear Structures ◽  
Unit Load ◽  
Complementary Energy ◽  
Finite Element Program ◽  
Unit Load Method ◽  
Element Program ◽  
Work Method

The unit load method, which is also known as a virtual work method, as well as by several other names, is a widely used tool for calculating deflections of linear structures. A procedure is developed here, which consists of similar steps and can be used when nonlinear material is involved. The formulae are developed based on the concept of complementary energy and the Castigliano theorem extended to nonlinear systems. A few simple examples are solved using this method and the results are compared with those obtained by a finite-element program. It appears that a blend of both types of analysis may be the optimal tool in many situations.

A Practical Method for the Rational Design of Ship Structures

1980 ◽  
Vol 24 (02) ◽  
pp. 101-113 ◽  
Author(s):  
Owen F. Hughes ◽  
Farrokh Mistree ◽  
Vedran Žanic
Keyword(s):  
Optimum Design ◽  
Rational Design ◽  
Cost Effective ◽  
Practical Method ◽  
General Purpose ◽  
Processing Unit ◽  
Ship Structures ◽  
Finite Element Program ◽  
Central Processing ◽  
Element Program

A practical, rationally based method is presented for the automated optimum design of ship structures. The method required the development of (a) a rapid, design-oriented finite-element program for the analysis of ship structures; (b) a comprehensive mathematical model for the evaluation of the capability of the structure; and (c) a cost-effective optimization algorithm for the solution of a large, highly constrained, nonlinear redesign problem. These developments have been incorporated into a program called SHIPOPT. The efficiency and robustness of the method is illustrated by using it to determine the optimum design of a complete cargo hold of a general-purpose cargo ship. The overall dimensions and the design loads are the same as those used in the design of the very successful SD14 series of ships. The redesign problem contains 94 variables, a nonlinear objective function, and over 500 constraints of which approximately half are non-linear. Program SHIPOPT required approximately eight minutes of central processing unit time on a CDC CYBER 171 to determine the optimum design.

Nonlinear Response and Failure of Steel Elbows Under In-Plane Bending and Pressure

2003 ◽  
Vol 125 (4) ◽  
pp. 393-402 ◽  
Author(s):  
S. A. Karamanos ◽  
E. Giakoumatos ◽  
A. M. Gresnigt
Keyword(s):  
Finite Element ◽  
Local Buckling ◽  
Shell Element ◽  
General Purpose ◽  
Element Analysis ◽  
Cross Sectional ◽  
Finite Element Program ◽  
Special Cases ◽  
Element Program ◽  
Plane Bending

The paper investigates the response of elbows under in-plane bending and pressure, through nonlinear finite element tools, supported by experimental results from real-scale tests. The finite element analysis is mainly based on a nonlinear three-node “tube element,” capable of describing elbow deformation in a rigorous manner, considering geometric and material nonlinearities. Furthermore, a nonlinear shell element from a general-purpose finite element program is employed in some special cases. Numerical results are compared with experimental data from steel elbow specimens. The comparison allows the investigation of important issues regarding deformation and ultimate capacity of elbows, with emphasis on relatively thin-walled elbows. The results demonstrate the effects of pressure and the influence of straight pipe segments. Finally, using the numerical tools, failure of elbows under bending moments is examined (cross-sectional flattening or local buckling), and reference to experimental observations is made.

Numerical Implementation of a Multi-Physical Fields Coupling Constitute Model

2013 ◽  
Vol 457-458 ◽  
pp. 354-357
Author(s):  
Yu Jie Sun ◽  
Qing Chun Cui ◽  
Suo Huai Zhang ◽  
Li Jun Yan
Keyword(s):  
Material Properties ◽  
General Purpose ◽  
Computational Method ◽  
Numerical Implementation ◽  
Temperature Dependent ◽  
Working Process ◽  
Finite Element Program ◽  
Element Program ◽  
User Material Subroutine ◽  
Constitute Model

The objective of this paper provides a numerical implementation procedure of thermo-metallurgical-mechanical constitute equation based on additively decomposition of strain rate. Together with phase transformation kinetics, the macro material properties are determined by assigning temperature dependent material properties to each phase and by applying mixture rule to combine. Then the constitute equation is implemented into general purpose implicit finite element program via user material subroutine. The effectiveness of developed computational method is confirmed by a Satoh test simulation. Simulation of Satoh test demonstrates that transformation induce plasticity has significant effect of the evolution of residual stress and can not be neglected for alloy steel during hot working process.

Muscle and Tendon Tissues: Constitutive Modeling and Computational Issues

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
L. A. Spyrou ◽  
N. Aravas
Keyword(s):  
Constitutive Model ◽  
Three Dimensional ◽  
General Purpose ◽  
Connective Tissues ◽  
Semitendinosus Muscle ◽  
Finite Element Program ◽  
Passive Behavior ◽  
Rate Dependent ◽  
Activation Level ◽  
Element Program

A three-dimensional constitutive model for muscle and tendon tissues is developed. Muscle and tendon are considered as composite materials that consist of fibers and the connective tissues and biofluids surrounding the fibers. The model is nonlinear, rate dependent, and anisotropic due to the presence of the fibers. Both the active and passive behaviors of the muscle are considered. The muscle fiber stress depends on the strain (length), strain-rate (velocity), and the activation level of the muscle, whereas the tendon fiber exhibits only passive behavior and the stress depends only on the strain. Multiple fiber directions are modeled via superposition. A methodology for the numerical implementation of the constitutive model in a general-purpose finite element program is developed. The current scheme is used for either static or dynamic analyses. The model is validated by studying the extension of a squid tentacle during a strike to catch prey. The behavior of parallel-fibered and pennate muscles, as well as the human semitendinosus muscle, is studied.

Quasi-Eulerian Finite Element Formulation for Fluid-Structure Interaction

1980 ◽  
Vol 102 (1) ◽  
pp. 62-69 ◽  
Author(s):  
T. Belytschko ◽  
J. M. Kennedy ◽  
D. F. Schoeberle
Keyword(s):  
Finite Element ◽  
Interaction Analysis ◽  
Fluid Structure Interaction ◽  
General Purpose ◽  
Element Formulation ◽  
Finite Element Program ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Eulerian Formulation ◽  
Element Program

A quasi-Eulerian formulation is developed for fluid-structure interaction analysis in which the fluid nodes are allowed to move independent of the material thus facilitating the treatment of problems with large structural motions. The governing equations are presented in general form and then specialized to two-dimensional plane and axisymmetric geometries. These elements have been incorporated in a general purpose transient finite element program and results are presented for two problems and compared to experimental results.

A Design Oriented Approach to Creep and Plasticity in Finite Element Programs

1971 ◽  
Vol 93 (3) ◽  
pp. 793-798 ◽  
Author(s):  
E. A. Wilson
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Duty Cycle ◽  
Natural Extension ◽  
Initial Strain ◽  
Loading Conditions ◽  
Finite Element Program ◽  
Element Program ◽  
Turbine Disks ◽  
Oriented Approach

This paper presents procedures for introducing plasticity and creep into finite element programs. The plasticity method described is intended for the designer who is interested in the stress distribution under prescribed loading conditions. The plasticity method uses a “relaxing approach” with initial strain equations. As a natural extension of the initial strain equations, creep is also presented. With both plasticity and creep available, a finite element program can be used to examine the stresses during the duty cycle of a piece of hardware. Examples of highly stressed turbine disks are shown.

Elastic Analysis of Journal Bearings

Volume 1 ◽  
2004 ◽  
Author(s):  
M. M. Villar ◽  
M. M. Pe´rez
Keyword(s):  
Stress Distribution ◽  
General Purpose ◽  
Von Mises Stress ◽  
Elastic Analysis ◽  
Stress Distributions ◽  
Finite Element Program ◽  
Relative Significance ◽  
Element Program ◽  
Von Mises ◽  
Hoop Stresses

In this paper a numerical model is used to investigate the effect of the elasticity of the bearing in the pressure distribution in the lubricant and the stress distribution in the bearing. The lubricant film, as well as a bearing, including the lining and the backing of the insert, and the housing, are modeled using the general-purpose ANSYS®5.7 commercial Finite Element program. Results have been obtained for the pressure, radial displacement, hoop and von Mises stress distributions at the surface of the bearing, as well as for the shear stress distribution at the interface between the lining and the backing. A number of conclusions have been drawn regarding the relative significance of the steep pressure gradient at the end of the lubricated region on the hoop stresses that cause localized bending distortions at the surface of the lining. These localized bending distortions, in turn, are likely to cause fatigue failure of the lining.

scholarly journals Harnessing Seeded Geometric Imperfection to Design Cylindrical Shells With Tunable Elastic Postbuckling Behavior

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Nan Hu ◽  
Rigoberto Burgueño
Keyword(s):  
Cylindrical Shells ◽  
Maximum Load ◽  
General Purpose ◽  
Mode Switching ◽  
Postbuckling Behavior ◽  
Finite Element Program ◽  
Geometric Imperfection ◽  
Element Program ◽  
Adaptive Materials ◽  
Discrete Map

Geometric imperfection, known as a detrimental effect on the buckling load of cylindrical shells, has a new role under the emerging trend of using buckling for smart purposes. Eigenshape-based geometries were designed on the shell surface with the aim of tailoring the postbuckling response. Fourteen seeded geometric imperfection (SGI) cylinders were fabricated using polymer-based 3D printing, and their postbuckling responses were numerically simulated with a general-purpose finite element program. Results on the prototyped SGI cylinders showed a tunable elastic postbuckling response in terms of initial and final stiffness, the maximum load drop from mode switching, and the number of snap-buckling events. A response contour and discrete map is presented to show how the number of waves in the axial and circumferential directions in the seeded eigenshape imperfection can control the elastic postbuckling response. SGI cylinders provide diverse design opportunities for controllable unstable response and are good candidates for use in smart and adaptive materials/structures.

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