Relevant bibliographies by topics / Thin plate spline finite element method

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Thin plate spline finite element method'

Author: Grafiati
Published: 11 December 2022
Last updated: 26 January 2023

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Journal articles on the topic "Thin plate spline finite element method"

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Fang, Lishan, and Linda Stals. "Adaptive discrete thin plate spline smoother." ANZIAM Journal 62 (November 5, 2021): C45—C57. http://dx.doi.org/10.21914/anziamj.v62.15979.

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The discrete thin plate spline smoother fits smooth surfaces to large data sets efficiently. It combines the favourable properties of the finite element surface fitting and thin plate splines. The efficiency of its finite element grid is improved by adaptive refinement, which adapts the precision of the solution. It reduces computational costs by refining only in sensitive regions, which are identified using error indicators. While many error indicators have been developed for the finite element method, they may not work for the discrete smoother. In this article we show three error indicators adapted from the finite element method for the discrete smoother. A numerical experiment is provided to evaluate their performance in producing efficient finite element grids. References F. L. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. Pat. Anal. Mach. Int. 11.6 (1989), pp. 567–585. doi: 10.1109/34.24792. C. Chen and Y. Li. A robust method of thin plate spline and its application to DEM construction. Comput. Geosci. 48 (2012), pp. 9–16. doi: 10.1016/j.cageo.2012.05.018. L. Fang. Error estimation and adaptive refinement of finite element thin plate spline. PhD thesis. The Australian National University. http://hdl.handle.net/1885/237742. L. Fang. Error indicators and adaptive refinement of the discrete thin plate spline smoother. ANZIAM J. 60 (2018), pp. 33–51. doi: 10.21914/anziamj.v60i0.14061. M. F. Hutchinson. A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines. Commun. Stat. Simul. Comput. 19.2 (1990), pp. 433–450. doi: 10.1080/0361091900881286. W. F. Mitchell. A comparison of adaptive refinement techniques for elliptic problems. ACM Trans. Math. Soft. 15.4 (1989), pp. 326–347. doi: 10.1145/76909.76912. R. F. Reiniger and C. K. Ross. A method of interpolation with application to oceanographic data. Deep Sea Res. Oceanographic Abs. 15.2 (1968), pp. 185–193. doi: 10.1016/0011-7471(68)90040-5. S. Roberts, M. Hegland, and I. Altas. Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. SIAM J. Numer. Anal. 41.1 (2003), pp. 208–234. doi: 10.1137/S0036142901383296. D. Ruprecht and H. Muller. Image warping with scattered data interpolation. IEEE Comput. Graphics Appl. 15.2 (1995), pp. 37–43. doi: 10.1109/38.365004. E. G. Sewell. Analysis of a finite element method. Springer, 2012. doi: 10.1007/978-1-4684-6331-6. L. Stals. Efficient solution techniques for a finite element thin plate spline formulation. J. Sci. Comput. 63.2 (2015), pp. 374–409. doi: 10.1007/s10915-014-9898-x. O. C. Zienkiewicz and J. Z. Zhu. A simple error estimator and adaptive procedure for practical engineerng analysis. Int. J. Numer. Meth. Eng. 24.2 (1987), pp. 337–357. doi: 10.1002/nme.1620240206.
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WU, LAI-YUN, CHENG-HUNG WU, and HSU-HUI HUANG. "SHEAR BUCKLING OF THIN PLATES USING THE SPLINE COLLOCATION METHOD." International Journal of Structural Stability and Dynamics 08, no. 04 (2008): 645–64. http://dx.doi.org/10.1142/s0219455408002818.

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This paper presents a highly accurate method for analyzing the critical shear buckling load of thin elastic rectangular plates. The solutions are approximated by the extended spline collocation method (SCM). Using the quintic table in place of the complex quintic B-spline functions, one can easily formulate the field equation of shear buckling loads for a thin elastic rectangular plate. Through the generalized eigenvalue analysis, the shear buckling loads and mode shapes for the plate can be determined precisely. Numerical examples are given for the critical shear buckling load of plates with various combinations of boundary conditions, aspect ratios, and uni- and bi-directional compressive/tensile loadings. The solutions obtained by the SCM are compared with those by the finite element method, the Lagrangian multiplier method, and the extended Kantorovich method under several types of boundary conditions. Compared with the other methods, the proposed SCM is not only more accurate, but also easier for computation.
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Sun, Jianliang, Mengqian Sun, Yunjing Jiao, and Yanan Gao. "Study on Plate Straightening Process Based on Elastic-Plastic B Spline Finite Strip Method." Journal of Mechanics 36, no. 6 (2020): 737–47. http://dx.doi.org/10.1017/jmech.2020.16.

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ABSTRACTAn elastic-plastic B spline finite strip method is proposed to investigate the continuous plate straightening process in this paper. First, the B spline displacement function that satisfies the boundary conditions of simply supported end and free end of the strip element is established, and then the stress-strain matrix is established. Second, the set method of total stiffness matrix based on B spline finite strip method for plate straightening problem is proposed, and the influence of nodal line number and strip elements number on the sparsity of total stiffness matrix is analyzed. Third, the loads on the strip elements are taken as linear uniform distribution, and the transformation matrix between the equivalent linear load and the actual load of the strip element is established. At last, the plate straightening simulation of 11 rolls straightening machine is made based on the elastic-plastic B spline finite strip method, the calculated results agree with the measured results, which approves that the elastic-plastic B spline finite strip method established can be applied to the plate straightening process.
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Xue, Xiaofeng, Xuefeng Chen, Xingwu Zhang, Baijie Qiao, and Jia Geng. "Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification." Shock and Vibration 2016 (2016): 1–24. http://dx.doi.org/10.1155/2016/8618202.

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A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF). It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI) finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD) method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.
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Hosseini, Shahram, and Gholamhossein Rahimi. "Nonlinear Bending Analysis of Hyperelastic Plates Using FSDT and Meshless Collocation Method Based on Radial Basis Function." International Journal of Applied Mechanics 13, no. 01 (2021): 2150007. http://dx.doi.org/10.1142/s1758825121500071.

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This paper investigates the nonlinear bending analysis of a hyperelastic plate via neo-Hookean strain energy function. The first-order shear deformation plate theory (FSDPT) is used for the formulation of the field variables. Also, the nonlinear Lagrangian strains are considered via the right Cauchy–Green tensor. The governing equations and nonlinear boundary conditions are derived using Euler–Lagrange relations. The meshless collocation method based on radial basis function is used to discretize the governing equations of the hyperelastic plate. Square and circular plates are studied to evaluate the accuracy of the meshless collocation method based on thin-plate spline (TPS) and multiquadric (MQ) and logarithmic thin-plate spline (LTPS) radial basis function. Also, the results of the meshless method are compared to those of the finite element method. In some cases, the meshless method is more efficient than the finite element method due to no meshing. The linear and nonlinear natural boundary conditions are directly imposed on the stiffness matrix and are compared to each other. The maximum differences between linear and nonlinear natural boundary conditions are 1.43%. The von-Mises stress using meshless collocation method based on TPS basis function is compared to those of the finite element method.
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Fang, Lishan. "Error indicators and adaptive refinement of the discrete thin plate spline smoother." ANZIAM Journal 60 (June 24, 2019): C33—C51. http://dx.doi.org/10.21914/anziamj.v60i0.14061.

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The discrete thin plate spline is a data fitting and smoothing technique for large datasets. Current research only uses uniform grids for this discrete smoother, which may require a fine grid to achieve a certain accuracy. This leads to a large system of equations and high computational costs. Adaptive refinement adapts the precision of the solution to reduce computational costs by refining only in sensitive regions. The error indicator is an essential part of the adaptive refinement as it identifies whether certain regions should be refined. Error indicators are well researched in the finite element method, but they might not work for the discrete smoother as data may be perturbed by noise and not uniformly distributed. Two error indicators are presented: one computes errors by solving an auxiliary problem and the other uses the bounds of the finite element error. Their performances are evaluated and compared with 2D model problems.
 
 References H. Chui and A. Rangarajan. A new point matching algorithm for non-rigid registration. Comput. Vis. Image Und., 89 (23): 114141, 2003. doi:10.1016/S1077-3142(03)00009-2. W. F. Mitchell. A comparison of adaptive refinement techniques for elliptic problems. ACM T. Math. Software, 15 (4): 326347, 1989. doi:10.1145/76909.76912. S. Roberts, M. Hegland, and I. Altas. Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. SIAM J. Numer. Anal., 41(1):208234, 2003. doi:10.1137/S0036142901383296. G. Sewell. Analysis of a finite element method. Springer-Verlag, 1985. doi:10.1007/978-1-4684-6331-6. R. Sprengel, K. Rohr, and H. S. Stiehl. Thin-plate spline approximation for image registration. In P. IEEE EMBS, volume 3, pages 11901191. IEEE, 1996. doi:10.1109/IEMBS.1996.652767. L. Stals. Efficient solution techniques for a finite element thin plate spline formulation. J. Sci. Comput., 63(2):374409, 2015. doi:10.1007/s10915-014-9898-x. G. Wahba. Spline models for observational data, volume 59 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, 1990. doi:10.1137/1.9781611970128.
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Mo, Tian-Jing, Jun Huang, Shuang-Bei Li, and Hai Wu. "A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory." Mathematical Problems in Engineering 2020 (July 10, 2020): 1–22. http://dx.doi.org/10.1155/2020/2943705.

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A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.
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Kempthorne, Daryl Matthew, Ian W. Turner, and John A. Belward. "Computational strategies for surface fitting using thin plate spline finite element methods." ANZIAM Journal 54 (May 12, 2013): 56. http://dx.doi.org/10.21914/anziamj.v54i0.6337.

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Ye, J. Q. "Postbuckling Analysis of Plates Under Combined Loads by a Mixed Finite Element and Boundary Element Method." Journal of Pressure Vessel Technology 115, no. 3 (1993): 262–67. http://dx.doi.org/10.1115/1.2929526.

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The postbuckling behavior of thin plates under combined loads is studied in this paper by using a mixed boundary element and finite element method. The transverse and the in-plane deformation of the plates are analyzed by the boundary element method and the finite element method, respectively. Spline functions were used as the interpolation functions and shape functions in the solution of both methods. A quadratic rectangular spline element is adopted in the finite element procedure. Numerical results are given for typical problems to show the effectiveness of the proposed approach. The possibilities to extend the method developed in this paper to more complicated postbuckling problems are discussed in the concluding section.
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10

Cheng, Xian Guo, and Wei Jun Liu. "A New Method for Deformation of B-Spline Surfaces." Advanced Materials Research 139-141 (October 2010): 1260–63. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.1260.

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This paper presents an efficient method for deforming B-spline surfaces, based on the surface energy minimization. Firstly, using an analogy between the B-spline surface patch and the thin-plate element of the finite element method, and applying external forces on the surface with some given geometric constraints, the forces can locate on part of the surface or the surface. Then, the energy of the B-spline surface can change with the change of the forces. Finally, a new B-spline surface is generated by solving an optimization problem of change of the energy. The forces can be a single force, a distributed force and set of isolated force. The method can accomplish easily local deformation and total deformation of the B-spline surface.
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Dissertations / Theses on the topic "Thin plate spline finite element method"

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Kempthorne, Daryl Matthew. "The development of virtual leaf surface models for interactive agrichemical spray applications." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/84525/12/84525%28thesis%29.pdf.

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This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered.
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Larsson, Karl. "Finite Element Methods for Thin Structures with Applications in Solid Mechanics." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-79297.

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Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy. In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings. The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus. In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.
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FEI, Baowei. "Image Registration for the Prostate." Case Western Reserve University School of Graduate Studies / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=case1224274091.

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Fayolle, Séverine. "Sur l'analyse numérique de raccords de poutres et de plaques." Paris 6, 1987. http://www.theses.fr/1987PA066005.

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Formulation mécanique, mathématique et numérique des problèmes de raccord de structures minces constituées d'assemblages de poutres ou de plaques avec deux types de charnières: rigides ou élastiques. Démonstration de l'existence et unicité d'une solution pour les problèmes continus, avec convergence de la solution élastique vers la rigide quand l'élasticité diminue. Approximation des solutions par une méthode conforme d'éléments finis.
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Fang, Lishan. "Error Estimation and Adaptive Refinement of Finite Element Thin Plate Spline." Phd thesis, 2021. http://hdl.handle.net/1885/237742.

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The thin plate spline smoother is a data fitting and smoothing technique that captures important patterns of potentially noisy data. However, it is computationally expensive for large data sets. The finite element thin plate spline smoother (TPSFEM) combines the thin plate spline smoother and finite element surface fitting to efficiently interpolate large data sets. When the TPSFEM uses uniform finite element grids, it may require a fine grid to achieve the desired accuracy. Adaptive refinement uses error indicators to identify sensitive regions and adapts the precision of the solution dynamically, which reduces the computational cost to achieve the required accuracy. Traditional error indicators were developed for the finite element method to approximate partial differential equations and may not be applicable for the TPSFEM. We examined techniques that may indicate errors for the TPSFEM and adapted four traditional error indicators that use different information to produce efficient adaptive grids. The iterative adaptive refinement process has also been adjusted to handle additional complexities caused by the TPSFEM. The four error indicators presented in this thesis are the auxiliary problem error indicator, recovery-based error indicator, norm-based error indicator and residual-based error indicator. The auxiliary problem error indicator approximates the error by solving auxiliary problems to evaluate approximation quality. The recovery-based error indicator calculates the error by post-processing discontinuous gradients of the TPSFEM. The norm-based error indicator uses an error bound on the interpolation error to indicate large errors. The residual-based error indicator computes interior element residuals and jumps of gradients across elements to estimate the energy norm of the error. Numerical experiments were conducted to evaluate the error indicators' performance on producing efficient adaptive grids, which are measured by the error versus the number of nodes in the grid. A set of one and two-dimensional model problems with various features are chosen to examine the effectiveness of the error indicators. As opposed to the finite element method, error indicators of the TPSFEM may also be affected by noise, data distribution patterns, data sizes and boundary conditions, which are assessed in the experiments. It is found that adaptive grids are significantly more efficient than uniform grids for two-dimensional model problems with difficulties like peaks and singularities. While the TPSFEM may not recover the original solution in the presence of noise or scarce data, error indicators still produce more efficient grids. We also learned that the difference is less obvious when the data has mostly smooth or oscillatory surfaces. Some error indicators that use data may be affected by data distribution patterns and boundary conditions, but the others are robust and produce stable results. Our error indicators also successfully identify sensitive regions for one-dimensional data sets. Lastly, when errors of the TPSFEM cannot be further reduced due to factors like noise, new stopping criteria terminate the iterative process aptly.
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Hancock, Penelope. "Finite element approximation of minimum generalised cross validation bivariate thin plate smoothing splines." Phd thesis, 2002. http://hdl.handle.net/1885/148534.

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Liao, Hong-jhe, and 廖宏哲. "The study of two dimensional B-Spline finite element method on irregular boundary shape and the application on plate analysis." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/90342187757862642489.

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碩士<br>國立成功大學<br>機械工程學系碩博士班<br>95<br>B-Spline finite element method is a numerical method which using B-Spline basis functions instead of finite element method basis function. The state variables of the B-Spline functions have Ck-2 continuity, where k is the order of the polynomials in B-Spline functions plus one. In order to enable the basis functions have Ck-2 continuity at boundaries between every cell, we should make the size of each cell the same. The cell is the square subdomain used for integration. The computational geometry theory used in this study is the Binary space partition. This method will spilt the polygon and we can use this property to proceed Boolean operation of geometric polygon. The cell mesh of the geometric polygon in the analysis is the results of a series of intersection test to the irregular geometric polygon. The program will deal with the boundaries between the polygon and intersected cell, and spilt the geometric solids included in the cell. We analyze the regular and the irregular shape plates in the two dimensional problems. In these plate examples, we find that the accuracy of the displacements and the stresses of B-Spline finite element method are almost the same as in the finite element method, but the degree of freedom in B-Spline finite element method is much less than finite element method.
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Books on the topic "Thin plate spline finite element method"

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Michel, Salaun, ed. Mathematical analysis of thin plate models. Springer, 1996.

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L, Krantz T., and United States. National Aeronautics and Space Administration., eds. Minimization of the vibration energy of thin-plate structures and the application to the reduction of gearbox vibration. National Aeronautics and Space Administration, 1995.

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L, Krantz T., and United States. National Aeronautics and Space Administration., eds. Minimization of the vibration energy of thin-plate structures and the application to the reduction of gearbox vibration. National Aeronautics and Space Administration, 1995.

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Book chapters on the topic "Thin plate spline finite element method"

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Kubiak, Tomasz. "Finite Element Method." In Static and Dynamic Buckling of Thin-Walled Plate Structures. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00654-3_4.

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Long, Yu-Qiu, and Si Yuan. "Spline Element II — Analysis of Plate/Shell Structures." In Advanced Finite Element Method in Structural Engineering. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00316-5_19.

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Long, Zhi-Fei, and Song Cen. "Generalized Conforming Thin Plate Element I—Introduction." In Advanced Finite Element Method in Structural Engineering. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00316-5_5.

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Mukhopadhyay, Madhujit, and Abdul Hamid Sheikh. "Semi-analytical and Spline Finite Strip Method of Analysis of Plate Bending." In Matrix and Finite Element Analyses of Structures. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08724-0_13.

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Long, Zhi-Fei, and Song Cen. "Generalized Conforming Thin Plate Element II—Line-Point and SemiLoof Conforming Schemes." In Advanced Finite Element Method in Structural Engineering. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00316-5_6.

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Cen, Song, and Zhi-Fei Long. "Generalized Conforming Thin Plate Element III — Perimeter-Point and Least-Square Conforming Schemes." In Advanced Finite Element Method in Structural Engineering. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00316-5_7.

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Ismail, N., Z. M. Hafizi, C. K. E. Nizwan, and S. Ali. "Interactions of Lamb Waves with Defects in a Thin Metallic Plate Using the Finite Element Method." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-7309-5_19.

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"Elastic Thin Plate." In The Finite Element Method. John Wiley & Sons Singapore Pte. Ltd, 2018. http://dx.doi.org/10.1002/9781119107323.ch10.

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Zienkiewicz, O. C., R. L. Taylor, and J. Z. Zhu. "Plate Bending Approximation: Thin and Thick Plates." In The Finite Element Method: its Basis and Fundamentals. Elsevier, 2013. http://dx.doi.org/10.1016/b978-1-85617-633-0.00013-7.

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Ciqian, Wu, and Wang Zhehui. "Error Estimate in Non-equi-mesh Spline Finite Strip Method for Thin Plate Bending Problem." In Functional Analysis, Approximation Theory and Numerical Analysis. WORLD SCIENTIFIC, 1994. http://dx.doi.org/10.1142/9789814360166_0010.

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Conference papers on the topic "Thin plate spline finite element method"

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Xiong, Guanglei. "Landmark-based registration from thin plate spline to B-spline with incompressible and diffeomorphic constraints using finite element method." In SPIE Medical Imaging, edited by David R. Haynor and Sébastien Ourselin. SPIE, 2012. http://dx.doi.org/10.1117/12.905008.

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Geng, Jia, Xingwu Zhang, Xuefeng Chen, and Xiaofeng Xue. "High-Frequency Vibration Analysis of Thin Plate Based on B-Spline Wavelet on Interval Finite Element Method." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65487.

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For the dynamic analysis of thin plate bending problems, the Finite Element Methods (FEMs) are the most commonly used numerical techniques in engineering. However, due to the deficiency of low computing efficiency and accuracy, the FEMs can’t be directly used to effectively evaluate dynamic analysis of thin plate with high modal density within low-high frequency domain. In order to solve this problem, the Wavelet Finite Element Methods (WFEMs) has been introduced to solve the problem by improving the computing efficiency and accuracy in this paper. Due to the properties of multi-resolution, the WFEMs own excellently high computing efficiency and accuracy for structure analysis. Furthermore, for the destination of predicting dynamic response of thin plate within high frequency domain, this paper introduces the Multi-wavelet element method based on c1 type wavelet thin plate element and a new assembly procedure to significantly promote the calculating efficiency and accuracy which aim at breaking up the limitation of frequency domain when using the existing WFEMs and traditional FEMs. Besides, the numerical studies are applied to certify the validity of the method by predicting state response of thin plate within 0∼1000Hz based on a special numerical example with high modal density. According to the literature, the frequency domain between 0 to 1000Hz contains the low-high frequency domain aiming at the numerical example. The numerical results show excellent agreement with the reference solutions captured by FEM and analytical expressions respectively. Among these, it is noteworthy that the relative errors between the analytical solutions and numerical solution are less than 0.4% when the dynamic response involved with 1000 modes.
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Carminelli, Antonio, and Giuseppe Catania. "Free Vibration Analysis of Double Curvature Thin Walled Structures by a B-Spline Finite Element Approach." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41904.

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This paper presents a free vibration analysis of general double curvature shell structures using B-spline shape functions and a refinement technique. The shell formulation is developed following the well known Ahmad degenerate approach including the effect of the shear deformation. The formulation is not isoparametric, as a consequence the assumed displacement field is described through non-uniform B-spline functions of any degree. A solution refinement technique is considered by means of a high continuity p-method approach. The eigensolution of a plate, and of single and double curvature shells are obtained by numerical simulation to test the performance of the approach. Solutions are compared with other available analytical and numerical solutions, and discussion follows.
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Kumar, Goldy, and Vadim Shapiro. "Reduced Material Model of Composite Laminates for 3D Finite Element Analysis." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35230.

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Laminate composites are widely used in automotive, aerospace, medical, and increasingly in consumer industries, due to their reduced weight, superior structural properties and cost-effectiveness. However, structural analysis of complex laminate structures remains challenging. 2D finite element methods based on plate and shell theories may be accurate and efficient, but they generally do not apply to the whole structure, and require identification and preprocessing (dimensional reduction) of the regions where the underlying assumptions hold. Differences in and limitations of theories for thin/thick plates and shells further complicate modeling and simulation of composites. Fully automated structural analysis using 3D elements with sufficiently high order basis functions is possible in principle, but is rarely practiced due to the significant increase in computational integration cost in the presence of a large number of laminate plies. We propose to replace the actual layup of the laminate structure by a simplified material model, allowing for a substantial reduction of the computational cost of 3D FEA. The reduced model, under the usual assumptions made in lamination theory, has the same constitutive relationship as the corresponding 2D plate model of the original laminate, but requires only a small fraction of computational integration costs in 3D FEA. We describe implementation of 3D FEA using the reduced material model in a meshfree system using second order B-spline basis functions. Finally, we demonstrate its validity by showing agreement between computed and known results for standard problems.
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Tanaka, Michihiko, and Motoki Kobayashi. "Finite Element Technique for the Curved Beam Analysis: In-Plate Vibration of Curved Beam With Varying Cross Section." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0111.

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Abstract The purpose of this paper is to present details of an algorithm for performing the numerical analysis of in-plane free vibration problem of curved beam by using the finite element technique. Although the finite element techniques for the straight or flat structures such as rods, beams and plates are well established, the finite element formulation for curved beam has not yet been completely discussed because of analytical complexity of the beam. The analysis of curved beam is reduced to the coupled problems of the axial and the transverse components of forces, bending moments, displacements and slopes in the beam. Sabir and Ashwell have discussed the vibrations of a ring by using the shape functions (interpolation functions) based on simple strain functions[1]. The discrete element displacement method was applied to the vibrations of shallow curved beam by Dawe[2]. Suzuki et al have presented the power series expansions method for solving free vibration of curved beams[3]. Irie et al have used spline functions to analyse the in-plane vibration of the varying cross section beams supported at one end[4].
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Zareh, Mehrdad, and Xiaoping Qian. "A New Plate Formulation Based on Triangular Isogeometric Analysis." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85577.

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This paper presents application of rational triangular Bezier splines (rTBS) for developing Kirchhoff-Love plate elements in the context of isogeometric analysis. Triangular isogeometric analysis can provide the C1 continuity over the mesh including elements interfaces, a necessary condition in finite elements formulation based on Kirchhoff-Love shell and plate theory. Using rTBS and macro-element technique, we develop Kirchhoff-Love plate elements, investigate the convergence rate and apply the method on complex geometry. Obtained results demonstrate that the optimal convergence rate is achievable; moreover, this method is applicable to represent thin geometric models of complex topology or thin geometric models in which efficient local refinement is required.
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Gantoi, F. Marina, Michael A. Brown, and Ahmed A. Shabana. "ANCF Modeling of the Contact Geometry and Deformation in Biomechanics Applications." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70224.

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The purpose of this investigation is to demonstrate the use of the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation where penetrations and separations at the contact points are allowed, and the constraint contact formulation where the non-conformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.
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Haji Mohammadi, Mohammad, and A. Shamsai. "Meshless Solution of 2D Fluid Flow Problems by Subdomain Variational Method Using MLPG Method With Radial Basis Functions (RBFs)." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98286.

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This paper deals with the solution of two-dimensional fluid flow problems using the truly meshless Local Petrov-Galerkin (MLPG) method. The present method is a truly meshless method based only on a number of randomly located nodes. Radial basis functions (RBF) are employed for constructing trial functions in the local weighted meshless local Petrov-Galerkin method for two-dimensional transient viscous fluid flow problems. No boundary integration is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions due to satisfaction of kronecker delta property in RBFs. Three different radial basis functions (RBFs), i.e. Multiquadrics (MQ), Gaussian (EXP) and Thin Plate Splines (TPS) are examined and the selection of their shape parameters is studied based on closed-form solutions. The effect of quadrature domain size is also studied. The variational method is used for the development of discrete equations. The results are obtained for a two-dimensional model problem using three RBFs and compared with the results of finite element and exact methods. Results show that the proposed method is highly accurate and possesses no numerical difficulties.
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Stammen, Lisa, and Wolfgang Dornisch. "A mixed isogeometric plane stress and plane strain formulation with different continuities for the alleviation of locking." In VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12554.

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Isogeometric analysis was founded by Hughes et al. and tries to unify computer aided design (CAD) and finite element analysis (FEA) by using the same model for geometry representation and analysis. Therefore, non-uniform rational B-splines (NURBS) and other kinds of splines are used as shape functions of the finite elements. Due to the exact representation of the geometry, analysis results can be improved. Furthermore, many fast and numerically stable algorithms have been developed that exhibit favourable mathematical properties.In mixed formulations stresses and/or strains or pressures are approximated independently and in addition to the usual displacement approximation. Using such methods is more robust and offers more accurate results. Hence, mixed formulations are employed to solve incompressible elasticity problems for instance.Recent investigations have already combined isogeometric analysis and mixed formulations in order to benefit from the advantages of both methods.In this contribution, a mixed isogeometric method is proposed in order to improve the analysis results and to counteract locking. Therefore, spline basis functions are used and the displacement shape functions of a two-dimensional isogeometric plane stress and plane strain element are supplemented by independent stress shape functions. These additional stress shape functions are chosen to be of one order lower compared to the displacement shape functions, but with adapted continuity.Evaluating the error norms for several examples, it is shown that the proposed mixed method leads to an improved accuracy of results compared to a standard isogeometric formulation and is able to counteract locking. Furthermore, the influence of the continuity of the stress shape functions is shown.
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Kumar, Ashok V., and Prem Dheepak Salem Periyasamy. "Analysis of Shell-Like Structures Using Structured Mesh." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28583.

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Shell-like structures are modeled in traditional finite element method using shell elements. The geometry for such structures is modeled using surfaces that represent the mid-plane. A mesh consisting of planar or curved shell elements is then generated for the surface which can be challenging for complex surface geometries and the resultant mesh sometimes poorly approximates the geometry. In order to avoid the problems associated with mesh generation, several meshless methods and structured grid methods have been proposed in the past two decades. In this paper, a structured grid method called Implicit Boundary Finite Element Method (IBFEM) has been used for the analysis of shell-like structures. Three dimensional elements that use uniform B-spline approximation schemes for representing the solution are used to represent the displacement field. The surfaces representing shell passes through these elements and the equations of these surfaces are used to represent the geometry exactly. B-spline approximations can provide higher order solutions that have tangent and curvature continuity. Numerical examples are presented to demonstrate the performance of shell elements using IBFEM and B-spline approximation. The results are compared with traditional shell element solutions.
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