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Adaptive mesh refinement for finite element analysis of elastic buckling disturbance of circularly curved beams due to multiple micro-cracks damage
Yongliang Wang
This study aimed to overcome the challenging issues involved in providing high-precision eigensolutions. The accurate prediction of the buckling load bearing capacity…
This study aimed to overcome the challenging issues involved in providing high-precision eigensolutions. The accurate prediction of the buckling load bearing capacity under different crack damage locations, sizes and numbers, and analysing the influence mechanism of crack damage on buckling instability have become the needs of theoretical research and engineering practice. Accordingly, a finite element method was developed and applied to solve the elastic buckling load and buckling mode of curved beams with crack damage. However, the accuracy of the solution depends on the quality of mesh, and the solution inevitably introduces errors due to mesh. Therefore, the adaptive mesh refinement method can effectively optimise the mesh distribution and obtain high-precision solutions.
For the elastic buckling of circular curved beams with cracks, the section damage defect analogy scheme of a circular arc curved beam crack was established to simulate the crack size (depth), position and number. The h-version finite element mesh adaptive analysis method of the variable section Euler–Bernoulli beam was introduced to solve the elastic buckling problem of circular arc curved beams with crack damage. The optimised mesh and high-precision buckling load and buckling mode solutions satisfying the preset error tolerance were obtained.
The results of testing typical examples show that (1) the established section damage defect analogy scheme of circular arc curved beam crack can effectively realise the simulation of crack size (depth), position and number. The solution strictly satisfies the preset error tolerance; (2) the non-uniform mesh refinement in the algorithm can be adapted to solve the arbitrary order frequencies and modes of cracked cylindrical shells under the conditions of different ring wave numbers, crack positions and crack depths; and (3) the change in the buckling mode caused by crack damage is applicable to the study of elastic buckling under various curved beam angles and crack damage distribution conditions.
This study can provide a novel strategy for the adaptive mesh refinement for finite element analysis of elastic buckling of circular arc curved beams with crack damage. The adaptive mesh refinement method established in this study is fundamentally different from the conventional finite element method which employs the user experience to densify the meshes near the crack. It can automatically and flexibly generate a set of optimised local meshes by iteratively dividing the fine mesh near the crack, which can ensure the high accuracy of the buckling loads and modes. The micro-crack in curved beams is also characterised by weakening the cross-sectional stiffness to realise the characterisation of locations, depths and distributions of multiple crack damage, which can effectively analyse the disturbance behaviour of different forms of micro-cracks on the dynamic behaviour of beams.
Engineering Computations, vol. ahead-of-print no. ahead-of-print
Crack damage
Circularly curved beams
Elastic buckling
Superconvergent patch recovery
Adaptive mesh refinement
Mesh refinement of finite element method for free vibration analysis of variable geometrical rotating cylindrical shells
This study aims to provide a reliable and effective algorithm that is suitable for addressing the problems of continuous orders of frequencies and modes under different…
This study aims to provide a reliable and effective algorithm that is suitable for addressing the problems of continuous orders of frequencies and modes under different boundary conditions, circumferential wave numbers and thickness-to-length ratios of moderately thick circular cylindrical shells. The theory of free vibration of rotating cylindrical shells is of utmost importance in fields such as structural engineering, rock engineering and aerospace engineering. The finite element method is commonly used to study the theory of free vibration of rotating cylindrical shells. The proposed adaptive finite element method can achieve a considerably more reliable high-precision solution than the conventional finite element method.
On a given finite element mesh, the solutions of the frequency mode of the moderately thick circular cylindrical shell were obtained using the conventional finite element method. Subsequently, the superconvergent patch recovery displacement method and high-order shape function interpolation techniques were introduced to obtain the superconvergent solution of the mode (displacement), while the superconvergent solution of the frequency was obtained using the Rayleigh quotient computation. Finally, the superconvergent solution of the mode was used to estimate the errors of the finite element solutions in the energy norm, and the mesh was subdivided to generate a new mesh in accordance with the errors.
In this study, a high-precision and reliable superconvergent patch recovery solution for the vibration modes of variable geometrical rotating cylindrical shells was developed. Compared with conventional finite element method, under the challenging varying geometrical circumferential wave numbers, and thickness–length ratios, the optimised finite element meshes and high-precision solutions satisfying the preset error limits were obtained successfully to solve the frequency and mode of continuous orders of rotating cylindrical shells with multiple boundary conditions such as simple and fixed supports, demonstrating good solution efficiency. The existing problem on the difficulty of adapting a set of meshes to the changes in vibration modes of different orders is finally overcome by applying the adaptive optimisation.
The approach developed in this study can accurately obtain the superconvergent patch recovery solution of the vibration mode of rotating cylindrical shells. It can potentially be extended to fine numerical models and high-precision computations of vibration modes (displacement field) and solid stress (displacement derivative field) for general structural special value problems, which can be extensively applied in the field of engineering computations in the future. Furthermore, the proposed method has the potential for adaptive analyses of shell structures and three-dimensional structures with crack damage. Compared with conventional finite element methods, significant advantages can be achieved by solving the eigenvalues of structures with high precision and stability.
Moderately thick circular cylindrical shell
Free vibration
A STUDY OF MESH OPTIMALITY CRITERIA IN ADAPTIVE FINITE ELEMENT ANALYSIS
E. OÑATE and G. BUGEDA
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the…
The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.
Mesh optimality
An expert system for forming quadrilateral finite elements
Y.C. Liu, H.A. ElMaraghy and K.F. Zhang
A knowledge‐based system for forming quadrilateral finite elements, XFORMQ, was developed at the Centre of Flexible Manufacturing Research and Development of McMaster…
A knowledge‐based system for forming quadrilateral finite elements, XFORMQ, was developed at the Centre of Flexible Manufacturing Research and Development of McMaster University, Canada. It automatically forms quadrilateral elements of good quality in conjunction with existing triangular mesh generators. XFORMQ can model geometries as complicated as those handled by triangular mesh generators. It allows for pre‐specified element sizes and rapid transition of element density. The concepts of 'layer' and 'polygon patterns', which considerably simplify the mesh generation rules and ensure the quality of formed elements, are introduced. Several test cases with different degrees of difficulties were used to evaluate XFORMQ's capabilities with satisfactory results. XFORMQ has the potential of generating meshes arising from the adaptive finite element analysis with quadrilateral elements.
Engineering Computations, vol. 7 no. 3
FINITE‐ELEMENT MESH GENERATION FROM GEOMETRIC MODELS
B. WÖrdenweber
This article describes a method for mesh generation, suitable for applications of the finite‐element method, which proceeds fully automatically from a geometric model of…
This article describes a method for mesh generation, suitable for applications of the finite‐element method, which proceeds fully automatically from a geometric model of the object provided by a CAD‐system. It first generates a coarse mesh which is then adapted to fit the finite‐element problem. A resulting system of equations can be solved by a Gaussian‐type matrix method with as few computations as are necessary for a well‐banded matrix, but without the need for node or element numbering.
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 2 no. 1
Gradient method for mesh refinement in compressible fluid flow simulations
Viktor Šajn, Dejan Nožak, Tadej Kosel and Franc Kosel
This paper aims to present an algorithm for local mesh refinement of finite elements in a two‐dimensional compressible fluid flow.
The algorithm works on a principle of maximum gradient of fluid variables, e.g. pressure, velocity and density. The simulation of two‐dimensional, transient, viscous, compressible, adiabatic flow of turbulent fluid through a De Laval nozzle was performed by the finite element method. The pressure gradient was used as a condition for mesh refinement.
With the gradient method faster numerical calculations can be obtained. Boundary layer separation and locations of normal shock waves can be described on locally refined mesh.
Further development of the algorithm is required, especially the determination of the gradient criterion.
The paper provides a new approach to mesh refinement. The mesh is refined automatically. Calculation time and required computer memory are decreased.
Aircraft Engineering and Aerospace Technology, vol. 79 no. 3
A metal‐forming approach to automatic generation of graded initial quadrilateral finite element meshes
S.B. Petersen, B.P.P.A. Gouveia, J.M.C. Rodrigues and P.A.F. Martins
This paper presents an algorithm for automatic generation of graded initial quadrilateral meshes targeted for the finite element analysis of metal‐forming processes…
This paper presents an algorithm for automatic generation of graded initial quadrilateral meshes targeted for the finite element analysis of metal‐forming processes. Meshing the domain geometry deals with a universe of shapes, and the procedure therefore takes into account the initial geometry of the billet. A grid‐based approach is utilised for generating an initial coarse mesh with well‐shaped (internal) elements, and in cases where non‐rectangular shapes are to be discretized, linking with the boundary is performed on the basis of constrained Delaunay triangulation. By analysing the contact situation between dies and mesh, an attempt is made to identify regions where plastic deformation is likely to be concentrated during the early stages of processing, and accordingly refinement of the mesh is performed locally by elemental subdivision. Simulation examples for closed‐die forging, forward rod and backward can extrusion substantiate the feasibility of this approach in terms of lowering the overall calculation error and limiting the interference between mesh and die.
Tooling mesh generation technique for iterative FEM die surface design algorithm to compensate for springback in sheetmetal stamping
Longwu Wu
FEM analysis has been increasingly employed to simulate sheetmetal forming processes for industrial application purposes. From the simulation results, finite element…
FEM analysis has been increasingly employed to simulate sheetmetal forming processes for industrial application purposes. From the simulation results, finite element analysts are able to predict the occurrences of splits and wrinkles therefore they can make recommendations of changes to the die design and/or to the part design to avoid possible stamping failures. The number of real die tryouts can be reduced, thus, the design cycle is shortened and manufacturing costs lowered. In the early times, application analysts were mostly concentrated on simulation of the stamping process itself starting from simple models, later running full size 3D models with large number of elements.
Axial claw pole motor: harmonic torque estimation using finite element method
Dominique Giraud, Baptiste Ristagno, Denis Netter, Julien Fontchastagner, Nicolas Labbe and Vincent Lanfranchi
This paper aims to propose a method to evaluate the information obtained on harmonics calculations and to estimate the precision of results using finite element method for…
This paper aims to propose a method to evaluate the information obtained on harmonics calculations and to estimate the precision of results using finite element method for an innovative motor topology in which some well-known meshing rules are difficult to apply.
The same magnetostatic problem is solved with several mesh sizes using both scalar and vector potentials magnetics formulations on a complex topology, an axial claw pole motor (ACPM). The proposed method lies in a comparison between the two weak formulations to determine what information is obtained on harmonics calculations and to estimate its precision. Moreover, an original mesh method is applied in the air gap to improve the numerical results.
The precision on harmonics calculations using finite element method on an ACPM is estimated. For the proposed motor and mesh, only the mean value (even with large mesh) and the first harmonic (with fine mesh) of torque are calculated with a good accuracy. This results confirm that the non-respect of the meshing rules have a strong impact on the results and that scalar and vector potentials magnetics formulations do not give exactly the same results. Before using torque harmonics values in vibration calculations, a finite element model has to be validated by using both fomulations.
This method is time-consuming and only applied on an ACPM in this work.
The axial claw pole motor, for which the classic meshing rules cannot be applied, is a complex topology very under-studied. To improve the calculation of space harmonics, the authors proposed to split the airgap into four parts. Then in the two central parts, the meshing step of the structured mesh is equal to the rotating step.
Axial flux machines
Claw pole motor
Patterns simulation in the 3D virtual stitching and try-on system
Guangzhou Zhu and Wenfang Song
The paper presents a method for the patterns simulation in the 3D virtual stitching and try-on system.
First, the patterns are designed using the garment CAD software and stored in the DXF format. Second, the regular grid method is employed to mesh the patterns to be quadrangular, and the patterns triangular meshing can be obtained by connecting the diagonal of the quadrangular. Then a mass-spring model is established, and the forces analysis and the explicit Euler integration method are employed to accomplish the patterns simulation. The paper demonstrates the robustness of our simulation through two sets of experiments, including a lady's dress patterns meshing experiments and the experiments of the virtual stitching of the lady's dress.
The patterns meshing algorithm can meet the requirements of the internal meshing and the boundary meshing, and it is very important to select an appropriate meshing density. The implementation of the virtual stitching of the lady's dress proves the effectiveness and usability of the simulation methods.
The lady's dress used in the experiments is a relatively simple fashion style, with only the front and back pattern. It is very worthy of further research on the effectiveness of the complex structure of clothing.
The paper includes practical implications of the methods of the patterns meshing and the virtual stitching of the simple fashion styles.
The simulation system is developed using VC++ 2015 with the help of the OpenGL functions library, which is proved as a simple, lower computation and robustness for the patterns simulation of the simple garments.
International Journal of Clothing Science and Technology, vol. 32 no. 6
DOI: https://doi.org/10.1108/IJCST-09-2019-0145
Patterns meshing
Regular grid method
Mass-spring model
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