scholarly journals FEM-PGD BASED TECHNIQUE FOR COLUMN SHAPE OPTIMIZATION AGAINST BUCKLING

2021 ◽  
Vol 11 (4) ◽  
pp. 143-159
Author(s):  
Tosporn Prasertsri ◽  
Supin Sartbumrung ◽  
Suneenut Suewongprayoon ◽  
Natdanai Sinsamutpadung ◽  
Jaroon Rungamornrat
Keyword(s):  
Finite Element ◽  
Shape Optimization ◽  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Numerical Procedure ◽  
Beam Theory ◽  
Rayleigh Quotient ◽  
Buckling Load ◽  
Cross Sectional ◽  
Good Convergence

This paper presents a simple numerical procedure based upon the projected gradient descent (PGD) and finite element method (FEM) for the shape optimization of laterally restrained columns to attain the maximum elastic buckling load under the specified volumetric constraint. The analysis of the buckling load is achieved via the formulation based on Euler-Bernoulli beam theory, the discretization by the standard finite element technique, and the determination of the least eigenvalue and the corresponding eigenvector via the power method with Rayleigh quotient. In the optimization, the profile of the cross-sectional area of the column is represented by piecewise polynomial interpolation functions. The gradient information and the projection operator required in PGD iterations are obtained explicitly in a closed form. A selected set of results is reported to demonstrate not only the good convergence behavior and accuracy of numerical solutions, but also the capability of the proposed technique to attain the optimal shape of columns for various scenarios.

Modelling of Rotating Twisted Blades as 1D Continuum

2016 ◽  
Vol 821 ◽  
pp. 183-190
Author(s):  
Jan Brůha ◽  
Drahomír Rychecký
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Beam Theory ◽  
Parameter Tuning ◽  
Finite Element Models ◽  
Cross Sectional ◽  
One Dimensional ◽  
Rayleigh Beam ◽  
Twisted Blade ◽  
Sectional Parameters

Presented paper deals with modelling of a twisted blade with rhombic shroud as one-dimensional continuum by means of Rayleigh beam finite elements with varying cross-sectional parameters along the finite elements. The blade is clamped into a rotating rigid disk and the shroud is considered to be a rigid body. Since the finite element models based on the Rayleigh beam theory tend to slightly overestimate natural frequencies and underestimate deflections in comparison with finite element models including shear deformation effects, parameter tuning of the blade is performed.

Design Innovation Size and Shape Optimization of a 1.0mm Multifunctional Forceps-Scissors Surgical Instrument

2008 ◽  
Vol 2 (1) ◽  
Author(s):  
Milton E. Aguirre ◽  
Mary Frecker
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shape Optimization ◽  
Optimization Problems ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Element Analysis ◽  
Cross Sectional ◽  
Size And Shape ◽  
The Cross

A size and shape optimization routine is developed for a 1.0mm diameter multifunctional instrument for minimally invasive surgery. The instrument is a compliant mechanism capable of both grasping and cutting. Multifunctional instruments are expected to be beneficial in the operating room because of their ability to perform multiple surgical tasks, thereby decreasing the total number of instrument exchanges in a single procedure. With fewer instrument exchanges, the risk of inadvertent tissue trauma as well as overall surgical time and costs are reduced. The focus of this paper is to investigate the performance effects of allowing the cross-sectional area along the length of the device to vary. This investigation is accomplished by defining various cross-sectional segments in terms of parametric variables and optimizing the dimensions of the instrument to provide a sufficient opening of the forceps jaws while maintaining adequate cutting and grasping forces. Two optimization problems are considered. First, all parametric segments are set equal to one another to achieve size optimization. Second, each segment is allowed to vary independently, thereby achieving shape optimization. Large deformation finite element analysis and optimization are conducted using ANSYS®. Finally, prototypes are fabricated using wire EMD and experiments are conducted to evaluate the instrument performance. As a result of allowing the cross-sectional area to vary, i.e., conducting shape optimization, the forceps and scissors blocked forces increased by as much as 83.2% and 87%, respectively. During prototype evaluations, it is found that the finite element analysis predictions were within 10% of the measured tool performance. Therefore, for this application, it is concluded that performing shape optimization does significantly influence the performance of the instrument.

scholarly journals Guided Waves in Thin-Walled Structural Members

2001 ◽  
Vol 123 (3) ◽  
pp. 376-382 ◽  
Author(s):  
A. H. Shah ◽  
W. Zhuang ◽  
N. Popplewell ◽  
J. B. C. Rogers
Keyword(s):  
Finite Element ◽  
Guided Waves ◽  
Polynomial Interpolation ◽  
Axial Direction ◽  
Thin Plates ◽  
Infinite Length ◽  
Structural Members ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Thin Walled

A semi-analytical finite element (SAFE) formulation is proposed to study the wave propagation characteristics of thin-walled members with an infinite length in the longitudinal (axial) direction. Common structural members are considered as an assemblage of thin plates. The ratio of the thickness of the plate to the wavelength in the axial direction is assumed to be small so that the plane-stress assumption is valid. Employing a finite element modeling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approximated by dividing the plates into several line (one-dimensional) segments and representing the generalized displacement distribution through the segment by polynomial interpolation functions. By applying Hamilton’s principle, the dispersion equation is obtained as a standard algebraic eigenvalue problem. The reasonably good accuracy of the method is demonstrated for the lowest modes by comparing, where feasible, the results with analytical solutions. To demonstrate the method’s versatility, frequency spectra are also presented for I and L shaped cross sections.

Nonorthogonal solution for thin-walled members – a finite element formulation

2006 ◽  
Vol 33 (4) ◽  
pp. 421-439 ◽  
Author(s):  
R Emre Erkmen ◽  
Magdi Mohareb
Keyword(s):  
Finite Element ◽  
Computational Cost ◽  
Beam Theory ◽  
Torsional Stiffness ◽  
Element Formulation ◽  
Field Equations ◽  
Cross Sectional ◽  
Special Cases ◽  
Thin Walled ◽  
Shell Finite Element

Conventional solutions for the equations of equilibrium based on the well-known Vlasov thin-walled beam theory uncouple the equations by adopting orthogonal coordinate systems. Although this technique considerably simplifies the resulting field equations, it introduces several modelling complications and limitations. As a result, in the analysis of problems where eccentric supports or abrupt cross-sectional changes exist (in elements with rectangular holes, coped flanges, or longitudinal stiffened members, etc.), the Vlasov theory has been avoided in favour of a shell finite element that offer modelling flexibility at higher computational cost. In this paper, a general solution of the Vlasov thin-walled beam theory based on a nonorthogonal coordinate system is developed. The field equations are then exactly solved and the resulting displacement field expressions are used to formulate a finite element. Two additional finite elements are subsequently derived to cover the special cases where (a) the St.Venant torsional stiffness is negligible and (b) the warping torsional stiffness is negligible. Key words: open sections, warping effect, finite element,thin-walled beams, asymmetric sections.

scholarly journals The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells

2016 ◽  
Vol 83 (11) ◽  
Author(s):  
Anna Lee ◽  
Francisco López Jiménez ◽  
Joel Marthelot ◽  
John W. Hutchinson ◽  
Pedro M. Reis
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Shell Theory ◽  
Numerical Solutions ◽  
Buckling Load ◽  
Quantitative Relation ◽  
Angular Width ◽  
Elastic Shells ◽  
Critical Buckling Load ◽  
Element Modeling

We study the effect of a dimplelike geometric imperfection on the critical buckling load of spherical elastic shells under pressure loading. This investigation combines precision experiments, finite element modeling, and numerical solutions of a reduced shell theory, all of which are found to be in excellent quantitative agreement. In the experiments, the geometry and magnitude of the defect can be designed and precisely fabricated through a customizable rapid prototyping technique. Our primary focus is on predictively describing the imperfection sensitivity of the shell to provide a quantitative relation between its knockdown factor and the amplitude of the defect. In addition, we find that the buckling pressure becomes independent of the amplitude of the defect beyond a critical value. The level and onset of this plateau are quantified systematically and found to be affected by a single geometric parameter that depends on both the radius-to-thickness ratio of the shell and the angular width of the defect. To the best of our knowledge, this is the first time that experimental results on the knockdown factors of imperfect spherical shells have been accurately predicted, through both finite element modeling and shell theory solutions.

On the Finite Element Modelling and Simulation of Carbon Nanotubes

2014 ◽  
Vol 607 ◽  
pp. 55-61 ◽  
Author(s):  
Ghasem Ghadyani ◽  
Mojtaba Akbarzade ◽  
Andreas Öchsner
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Beam Theory ◽  
Elastic Stiffness ◽  
Buckling Load ◽  
Timoshenko Beams ◽  
Bernoulli Beam ◽  
Critical Buckling Load ◽  
Beam Elements ◽  
Mesh Density

In this paper, two different beam elements (i.e. according to the Bernoulli beam and Timoshenko beam theory) for the modeling of the behavior of carbon nanotubes are applied. Finite element models are developed for this study with variation of chirality for both zig-zag and armchair configurations of CNTs. The deformations from the finite element simulations are subsequently used to predict the elastic stiffness and the critical buckling load in terms of material and geometric parameters. Furthermore, the dependence of mechanical properties on the kind of beam element and the mesh density is also compared. Based on the obtained results, Youngs modulus and critical buckling load of structures using Timoshenko beams are clearly lower than the Bernoulli beam approach for all chiralities.

An h-version adaptive FEM for eigenproblems in system of second order ODEs: vector Sturm-Liouville problems and free vibration of curved beams

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
High Precision ◽  
Numerical Solutions ◽  
Rayleigh Quotient ◽  
Second Order ◽  
Adaptive Finite Element Method ◽  
Multiple Cracks ◽  
Content Type ◽  
Sturm Liouville

Purpose This study aims to overcome the involved challenging issues and provide high-precision eigensolutions. General eigenproblems in the system of ordinary differential equations (ODEs) serve as mathematical models for vector Sturm-Liouville (SL) and free vibration problems. High-precision eigenvalue and eigenfunction solutions are crucial bases for the reliable dynamic analysis of structures. However, solutions that meet the error tolerances specified are difficult to obtain for issues such as coefficients of variable matrices, coincident and adjacent approximate eigenvalues, continuous orders of eigenpairs and varying boundary conditions. Design/methodology/approach This study presents an h-version adaptive finite element method based on the superconvergent patch recovery displacement method for eigenproblems in system of second-order ODEs. The high-order shape function interpolation technique is further introduced to acquire superconvergent solution of eigenfunction, and superconvergent solution of eigenvalue is obtained by computing the Rayleigh quotient. Superconvergent solution of eigenfunction is used to estimate the error of finite element solution in the energy norm. The mesh is then, subdivided to generate an improved mesh, based on the error. Findings Representative eigenproblems examples, containing typical vector SL and free vibration of beams problems involved the aforementioned challenging issues, are selected to evaluate the accuracy and reliability of the proposed method. Non-uniform refined meshes are established to suit eigenfunctions change, and numerical solutions satisfy the pre-specified error tolerance. Originality/value The proposed combination of methodologies described in the paper, leads to a powerful h-version mesh refinement algorithm for eigenproblems in system of second-order ODEs, that can be extended to other classes of applications in damage detection of multiple cracks in structures based on the high-precision eigensolutions.

Shear stress concentrations in tramway rails: Results from beam theory-based cross-sectional 2D Finite Element analyses

2019 ◽  
Vol 195 ◽  
pp. 579-590 ◽  
Author(s):  
Patricia Hasslinger ◽  
Aleš Kurfürst ◽  
Thomas Hammer ◽  
Edgar Fischmeister ◽  
Christian Hellmich ◽  
...  
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Beam Theory ◽  
Finite Element Analyses ◽  
Stress Concentrations ◽  
Cross Sectional
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