Application of Transition Finite Elements in hpq-Adaptive Modeling and Analysis of Machine Elements

AINSWORTH M., ODEN J.T. 1992. A procedure for a posteriori error estimation for h-p finite element methods. Computer Methods in Applied Mechanics and Engineering, 101: 73-96.   Google Scholar

COFER W.F., WILL K.M. 1991. A Three-dimensional, Shell-solid transition element for general nonlinear analysis. Computers & Structures, 38: 449-462.   Google Scholar

DÁVILA C.G.1994. Solid-to-shell transition elements for the computation of interlaminar stresses. Computing Systems in Engineering, 5: 193-202.   Google Scholar

DEMKOWICZ L. 2006. Computing with hp-Adaptive Finite Elements. Volume I. One and Two-Dimensional Elliptic and Maxwell Problems. Chapman &Hall/CRC Press, Taylor and Francis Group, Boca Raton.   Google Scholar

GMÜR T.C., SCHORDERET A.M. 1993. A set of three-dimensional solid to shell transition elements for structural dynamics. Computers & Structures, 46: 583-591.   Google Scholar

HUANG F., XIE X. 2011. A Modified Nonconforming 5-Node Quadrilateral Transition Finite Element. Advances in Applied Mathematics and Mechanics, 2: 784-797.   Google Scholar

JEYACHANDRABOSE C., KIRKHOPE J. 1984. Construction of transition finite elements for the plane triangular family. Computers & Structures, 18: 1127-1134.   Google Scholar

NOSARZEWSKA M. 2007. Zastosowanie elementów przejściowych w adaptacyjnej analizie struktur sprężystych. Praca magisterska. Wydział Nauk Technicznych, Uniwersytet Warmińsko-Mazurski, Olsztyn.   Google Scholar

NOSARZEWSKA M., ZBOIŃSKI G. 2009. Efektywność przejściowych elementów skończonych w hierarchicznym modelowaniu struktur złożonych. Modelowane Inżynierskie, 7(38): 131-138.   Google Scholar

ODEN J.T. 1993. Error estimation and control in computational fluid dynamics. The O.C. Zienkiewicz Lecture. Proc. Math. of Finite Elements - MAFELAP VIII, 1-36. Brunnel Univ., Uxbridge.   Google Scholar

ODEN J.T, CHO J.R. 1996. Adaptive hpq-finite element methods of hierarchical models for plate- and shell-like structures. Computer Methods in Applied Mechanics and Engineering, 136: 317-345.   Google Scholar

RANK E., BABUŠKA I. 1987. An expert system for the optimal mesh design in the hp-version of the finite element method. International Journal for Numerical Methods in Engineering, 24: 2087-2106.   Google Scholar

SCHWAB C. 1998. p and hp FEM. Oxford University Press, Oxford.   Google Scholar

SURANA K.S. 1980. Transition finite elements for three-dimensional stress analysis. International Journal for Numerical Methods in Engineering, 15: 991-1020.   Google Scholar

SURANA K.S. 1982. Geometrically non-linear formulation for the three dimensional solid-shell transition finite elements. Computers & Structures, 15: 549-566.   Google Scholar

SURANA K.S. 1983. Geometrically nonlinear formulation for the axi-simetric transition finite element. Computers & Structures, 17: 243-255.   Google Scholar

SURANA K.S. 1987. Three dimensional solid-shell transition finite elements for heat conduction. Computers & Structures, 26: 941-950.   Google Scholar

SZABÓ B.A., SAHRMANN G.J. 1998, Hierarchic plate and shell models based on p-extension. International Journal for Numerical Methods in Engineering, 26: 1855-1881.   Google Scholar

WAN K.H. 2004. Transition finite elements for mesh refinement in plane and plate Bendig analyses. MSc Thesis. Mechanical Engineering Department, The University of Hong Kong.   Google Scholar

ZBOIŃSKI G. 1997. Application of the three-dimensional triangular-prism hpq adaptive finite element to plate shell analysis. Computers and Structures, 65(4): 497-514.   Google Scholar

ZBOIŃSKI G. 2001. Modelowanie hierarchiczne i metoda elementów skończonych do adaptacyjnej analizy struktur złożonych. Zeszyty Naukowe IMP PAN w Gdańsku. Studia i Materiały. Instytut Maszyn Przepływowych PAN, Gdańsk.   Google Scholar

ZBOIŃSKI G. 2010. Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. Part 1. Hierarchical modeling and approximation. Computer Methods in Applied Mechanics and Engineering, 199: 2913-2940.   Google Scholar

ZBOIŃSKI G. 2013. Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. Part 2. A posteriori error estimation. Computer Methods in Applied Mechanics and Engineering, 267: 531-565.   Google Scholar

ZBOIŃSKI G., JASIŃSKI M. 2007. 3D-based hp-adaptive first-order shell finite element for modelling and analysis of complex structures. Part 1. The model and the approximation. International Journal for Numerical Methods in Engineering, 70: 1513-1545.   Google Scholar

ZBOIŃSKI G., OSTACHOWICZ W. 2000. An algorithm of a family of 3D-based, solid-to-shell, hpq/hp-adaptive finite elements. Journal of Theoretical and Applied Mechanics, 38: 791-806.   Google Scholar

ZIELIŃSKA M., ZBOIŃSKI G. 2013. Opracowanie efektywnego numerycznie sformułowania adaptacyjnego, opartego na podejściu trójwymiarowym, bryłowo-powłokowego elementu przejściowego zapewniającego ciągłość pola naprężeń pomiędzy modelami podstawowymi. Raport wewnętrzny, nr arch. 324/15, Instytut Maszyn Przepływowych PAN, Gdańsk.   Google Scholar

ZIELIŃSKA M., ZBOIŃSKI G. 2014a. Analiza płyt i powłok zdominowanych membranowo z ciągłą zmianą naprężeń i odkształceń w strefach przejściowych. Mechanik, 87: 855-872.   Google Scholar

ZIELIŃSKA M., ZBOIŃSKI G. 2014b. hp-Adaptive finite element analysis of thin-walled structures with use of the shell-to-shell transition elements. In: Recent Advances in Computational Mechanics. Eds. T. Lodygowski, J. Rakowski, P, Litewka. CRC Press, London.   Google Scholar