scholarly journals Adaptive finite element analysis for damage detection of non-uniform Euler–Bernoulli beams with multiple cracks based on natural frequencies

2018 ◽  
Vol 35 (3) ◽  
pp. 1203-1229 ◽  
Author(s):  
Yongliang Wang ◽  
Yang Ju ◽  
Zhuo Zhuang ◽  
Chenfeng Li
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Damage Detection ◽  
Crack Detection ◽  
Iteration Process ◽  
Adaptive Finite Element Method ◽  
Multiple Cracks ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Vibration Problems

Purpose This study aims to develop an adaptive finite element method for structural eigenproblems of cracked Euler–Bernoulli beams via the superconvergent patch recovery displacement technique. This research comprises the numerical algorithm and experimental results for free vibration problems (forward eigenproblems) and damage detection problems (inverse eigenproblems). Design/methodology/approach The weakened properties analogy is used to describe cracks in this model. The adaptive strategy proposed in this paper provides accurate, efficient and reliable eigensolutions of frequency and mode (i.e. eigenpairs as eigenvalue and eigenfunction) for Euler–Bernoulli beams with multiple cracks. Based on the frequency measurement method for damage detection, using the difference between the actual and computed frequencies of cracked beams, the inverse eigenproblems are solved iteratively for identifying the residuals of locations and sizes of the cracks by the Newton–Raphson iteration technique. In the crack detection, the estimated residuals are added to obtain reliable results, which is an iteration process that will be expedited by more accurate frequency solutions based on the proposed method for free vibration problems. Findings Numerical results are presented for free vibration problems and damage detection problems of representative non-uniform and geometrically stepped Euler–Bernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method. Originality/value The proposed combination of methodologies described in the paper leads to a very powerful approach for free vibration and damage detection of beams with cracks, introducing the mesh refinement, that can be extended to deal with the damage detection of frame structures.

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.

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

Adaptive finite element analysis of free vibration of elastic membranes via element energy projection technique

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Haohan Sun ◽  
Si Yuan
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Mesh Refinement ◽  
Error Tolerance ◽  
Maximum Norm ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Local Mesh Refinement ◽  
Elastic Membranes ◽  
Element Energy Projection

Purpose A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique. Design/methodology/approach By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems. Findings Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm. Originality/value By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.

scholarly journals ADAPTIVE FINITE ELEMENT STRATEGY FOR FREE VIBRATION PROBLEMS/PRISITAIKANČIOJI BAIGTINIŲ ELEMENTŲ STRATEGUA LAISVŲJŲ SVYRAVIMŲ UŽDAVINIAMS SPRĘSTI

1997 ◽  
Vol 3 (9) ◽  
pp. 26-33
Author(s):  
Romualdas Baušys
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Adaptive Finite Element ◽  
Vibration Problems

Norint rasti pageidaujamo tikslumo inžinerinių uždavinių sprendimus, naudojamos įvairios prisitaikančiosios baigtinių elementuų strategijos. Straipsnyje pateikta prisitaikančiosios baigtinių elementų strategijos h-versija, skirta laisvųjų svyravimų uždaviniams spręsti. Jos esmę sudaro naujo diskretizacijos tinklo generavimas, naudojant tos pačios eilės baigtinius elementus. Šios strategijos tikslas—sugeneruoti optimalų baigtinių elementų tinklą, kuris apibūdinamas tolygiu diskretizacijos paklaidų pasiskirstymu. Diskretizacijos paklaidos randamos poprocesoriniais lokaliniu ir globaliniu būdais. Atlikti skaitiniai eksperimentai atskleidė pasiūlytos prisitaikanšiosios baigtinių elementų strategijos efektyvmą, nes optimalus diskretizacijos tinklas buvo suformuotas kiekvienai tyrinėtai nuosavai reikšmei, panaudojant tiktai vieną algoritmo iteraciją.

scholarly journals Adaptive finite element method for eigensolutions of regular second and fourth order Sturm-Liouville problems via the element energy projection technique

2017 ◽  
Vol 34 (8) ◽  
pp. 2862-2876 ◽  
Author(s):  
Si Yuan ◽  
Kangsheng Ye ◽  
Yongliang Wang ◽  
David Kennedy ◽  
Frederic W. Williams
Keyword(s):  
Finite Element ◽  
Fourth Order ◽  
Variable Coefficients ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Fe Method ◽  
Eigenvalues And Eigenfunctions ◽  
Content Type ◽  
Sturm Liouville ◽  
Element Energy Projection

Purpose The purpose of this paper is to present a numerically adaptive finite element (FE) method for accurate, efficient and reliable eigensolutions of regular second- and fourth-order Sturm–Liouville (SL) problems with variable coefficients. Design/methodology/approach After the conventional FE solution for an eigenpair (i.e. eigenvalue and eigenfunction) of a particular order has been obtained on a given mesh, a novel strategy is introduced, in which the FE solution of the eigenproblem is equivalently viewed as the FE solution of an associated linear problem. This strategy allows the element energy projection (EEP) technique for linear problems to calculate the super-convergent FE solutions for eigenfunctions anywhere on any element. These EEP super-convergent solutions are used to estimate the FE solution errors and to guide mesh refinements, until the accuracy matches user-preset error tolerance on both eigenvalues and eigenfunctions. Findings Numerical results for a number of representative and challenging SL problems are presented to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method. Research limitations/implications The method is limited to regular SL problems, but it can also solve some singular SL problems in an indirect way. Originality/value Comprehensive utilization of the EEP technique yields a simple, efficient and reliable adaptive FE procedure that finds sufficiently fine meshes for preset error tolerances on eigenvalues and eigenfunctions to be achieved, even on problems which proved troublesome to competing methods. The method can readily be extended to vector SL problems.

Three Dimensional Dynamic Analyses on Stroller Wheel with Shock Absorber

2013 ◽  
Vol 387 ◽  
pp. 159-163
Author(s):  
Yi Chern Hsieh ◽  
Minh Hai Doan ◽  
Chen Tai Chang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
The Road ◽  
Dimensional Finite Element ◽  
On The Road ◽  
Three Dimensional Finite Element ◽  
Element Method

We present the analyses of dynamics behaviors on a stroller wheel by three dimensional finite element method. The vibration of the wheel system causes by two different type barriers on the road as an experiment design to mimic the real road conditions. In addition to experiment analysis, we use two different packages to numerically simulate the wheel system dynamics activities. Some of the simulation results have good agreement with the experimental data in this research. Other interesting data will be measured and analyzed by us for future study and we will investigate them by using adaptive finite element method for increasing the precision of the computation results.

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