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Published in: Meccanica 4-5/2018

13-10-2017

An efficient flat shell element

Authors: Mohammad Rezaiee-Pajand, Majid Yaghoobi

Published in: Meccanica | Issue 4-5/2018

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Abstract

Up to now, various flat shell’s elements are created by combining plane and bending plate elements. In the case of complicated problems with coarse distorted mesh, only using efficient element leads to the accurate responses. These kinds of the elements are insensitive to the distortion. In fact, they can identify and remove the related errors. In this paper, two internal and boundary fields are deployed in a hybrid functional for formulating the proposed plane element. The method is established based on the optimum strain states. Furthermore, Trefftz functionals for independent internal and boundary fields are employed to formulate the suggested bending element. In this procedure, the optimum strain states construct the internal field, and element’s boundary field is achieved by considering the beam behavior. Finally, the high efficiency of author’s element is assessed by solving several numerical samples.

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Literature
1.
go back to reference Gal E, Levy R (2006) Geometrically nonlinear analysis structures using a flat triangular element. Arch Comput Methods Eng 13:331–388CrossRefMATH Gal E, Levy R (2006) Geometrically nonlinear analysis structures using a flat triangular element. Arch Comput Methods Eng 13:331–388CrossRefMATH
2.
go back to reference Zhang YX, Kim KS (2005) Linear and geometrically nonlinear analysis of plates and shells by a new refined nonconforming triangular plate/shell element. Comput Mech 36:331–342MathSciNetCrossRefMATH Zhang YX, Kim KS (2005) Linear and geometrically nonlinear analysis of plates and shells by a new refined nonconforming triangular plate/shell element. Comput Mech 36:331–342MathSciNetCrossRefMATH
3.
go back to reference Zhang Y, Zhou H, Li J, Feng W, Li D (2011) A 3-node flat triangular shell element with corner drilling freedoms and transverse shear correction. Int J Numer Methods Eng 86:1413–1434MathSciNetCrossRefMATH Zhang Y, Zhou H, Li J, Feng W, Li D (2011) A 3-node flat triangular shell element with corner drilling freedoms and transverse shear correction. Int J Numer Methods Eng 86:1413–1434MathSciNetCrossRefMATH
4.
go back to reference Felippa CA (2003) A study of optimal membrane triangles with drilling freedoms. Comput Methods Appl Mech Eng 192:2125–2168ADSCrossRefMATH Felippa CA (2003) A study of optimal membrane triangles with drilling freedoms. Comput Methods Appl Mech Eng 192:2125–2168ADSCrossRefMATH
6.
go back to reference Felippa CA (2004) A template tutorial. In: Mathisen KM, Kvamsdal T, Okstad KM (eds) Computational mechanics: theory and practice. CIMNE, Barcelona, pp 29–68 Felippa CA (2004) A template tutorial. In: Mathisen KM, Kvamsdal T, Okstad KM (eds) Computational mechanics: theory and practice. CIMNE, Barcelona, pp 29–68
7.
8.
go back to reference Rezaiee-Pajand M, Yaghoobi M (2013) A free of parasitic shear strain formulation for plane element. Res Civ Environ Eng 1:1–27 Rezaiee-Pajand M, Yaghoobi M (2013) A free of parasitic shear strain formulation for plane element. Res Civ Environ Eng 1:1–27
9.
go back to reference Rezaiee-Pajand M, Yaghoobi M (2014) An efficient formulation for linear and geometric non-linear membrane elements. Lat Am J Solids Struct 11:1012–1035CrossRef Rezaiee-Pajand M, Yaghoobi M (2014) An efficient formulation for linear and geometric non-linear membrane elements. Lat Am J Solids Struct 11:1012–1035CrossRef
10.
go back to reference Rezaiee-Pajand M, Yaghoobi M (2014) A robust triangular membrane element. Lat Am J Solids Struct 11:2648–2671CrossRef Rezaiee-Pajand M, Yaghoobi M (2014) A robust triangular membrane element. Lat Am J Solids Struct 11:2648–2671CrossRef
11.
go back to reference Rezaiee-Pajand M, Yaghoobi M (2015) Two new quadrilateral elements based on strain states. Civ Eng Infrastruct J 48(1):133–156 Rezaiee-Pajand M, Yaghoobi M (2015) Two new quadrilateral elements based on strain states. Civ Eng Infrastruct J 48(1):133–156
12.
go back to reference Cen S, Zhou MJ, Fu XR (2011) A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions. Comput Struct 89:517–528CrossRef Cen S, Zhou MJ, Fu XR (2011) A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions. Comput Struct 89:517–528CrossRef
13.
go back to reference Choo YS, Choi N, Lee BC (2006) Quadrilateral and triangular plane elements with rotational degrees of freedom based on the hybrid Trefftz method. Finite Elem Anal Des 42:1002–1008CrossRef Choo YS, Choi N, Lee BC (2006) Quadrilateral and triangular plane elements with rotational degrees of freedom based on the hybrid Trefftz method. Finite Elem Anal Des 42:1002–1008CrossRef
14.
go back to reference Choi N, Choo YS, Lee BC (2006) A hybrid Trefftz plane elasticity element with drilling degrees of freedom. Comput Methods Appl Mech Eng 195:4095–4105ADSCrossRefMATH Choi N, Choo YS, Lee BC (2006) A hybrid Trefftz plane elasticity element with drilling degrees of freedom. Comput Methods Appl Mech Eng 195:4095–4105ADSCrossRefMATH
15.
go back to reference MacNeal RH, Harder RL (1988) A refined four-noded membrane element with rotational degrees of freedom. Comput Struct 28(1):75–84CrossRefMATH MacNeal RH, Harder RL (1988) A refined four-noded membrane element with rotational degrees of freedom. Comput Struct 28(1):75–84CrossRefMATH
16.
go back to reference Tian R, Yagawa G (2007) Allman’s triangle, rotational DOF and partition of unity. Int J Numer Methods Eng 69:837–858CrossRefMATH Tian R, Yagawa G (2007) Allman’s triangle, rotational DOF and partition of unity. Int J Numer Methods Eng 69:837–858CrossRefMATH
17.
go back to reference Huang M, Zhao Z, Shen C (2010) An effective planar triangular element with drilling rotation. Finite Elem Anal Des 46:1031–1036CrossRef Huang M, Zhao Z, Shen C (2010) An effective planar triangular element with drilling rotation. Finite Elem Anal Des 46:1031–1036CrossRef
18.
go back to reference Allman DJ (1984) Compatible triangular element including vertex rotations for plane elasticity analysis. Comput Struct 19:1–8CrossRefMATH Allman DJ (1984) Compatible triangular element including vertex rotations for plane elasticity analysis. Comput Struct 19:1–8CrossRefMATH
20.
go back to reference Felippa CA (2009) Advanced finite element methods, 4th edn. Mubeen-UET, Lahore Felippa CA (2009) Advanced finite element methods, 4th edn. Mubeen-UET, Lahore
21.
22.
go back to reference Jirousek J, Guex L (1986) The hybrid-Trefftz finite element model and its application to plate bending. Int J Numer Methods Eng 23:651–693MathSciNetCrossRefMATH Jirousek J, Guex L (1986) The hybrid-Trefftz finite element model and its application to plate bending. Int J Numer Methods Eng 23:651–693MathSciNetCrossRefMATH
23.
24.
go back to reference Jirousek J (1987) Hybid Trefftz plate bending elements with p-method capabilities. Int J Numer Methods Eng 24:1367–1393CrossRefMATH Jirousek J (1987) Hybid Trefftz plate bending elements with p-method capabilities. Int J Numer Methods Eng 24:1367–1393CrossRefMATH
25.
go back to reference Allman DJ (1984) A compatible triangular element including vertex rotations for plane elasticity analysis. Comput Struct 19:1–8CrossRefMATH Allman DJ (1984) A compatible triangular element including vertex rotations for plane elasticity analysis. Comput Struct 19:1–8CrossRefMATH
26.
go back to reference Cook RD (1993) Further development of a three-node triangular shell element. Int J Numer Methods Eng 36(8):1413–1425CrossRefMATH Cook RD (1993) Further development of a three-node triangular shell element. Int J Numer Methods Eng 36(8):1413–1425CrossRefMATH
27.
go back to reference Providas E, Kattis MA (2000) An assessment of two fundamental flat triangular shell elements with drilling rotations. Comput Struct 77(2):129–139CrossRef Providas E, Kattis MA (2000) An assessment of two fundamental flat triangular shell elements with drilling rotations. Comput Struct 77(2):129–139CrossRef
28.
go back to reference Carpenter N, Stolarski H, Belytschko T (1986) Improvements in 3-node triangular shell elements. Int J Numer Methods Eng 23:1643–1667CrossRefMATH Carpenter N, Stolarski H, Belytschko T (1986) Improvements in 3-node triangular shell elements. Int J Numer Methods Eng 23:1643–1667CrossRefMATH
29.
go back to reference Stress analysis reference manual (1993) In MF/WARP 3D Warpage Analysis Release 3.0. Moldflow Pty. Ltd Stress analysis reference manual (1993) In MF/WARP 3D Warpage Analysis Release 3.0. Moldflow Pty. Ltd
30.
go back to reference Kim JG, Lee JK, Park YK (2002) A new 3-node triangular-at shell element. Commun Numer Methods Eng 18:153–159CrossRefMATH Kim JG, Lee JK, Park YK (2002) A new 3-node triangular-at shell element. Commun Numer Methods Eng 18:153–159CrossRefMATH
31.
go back to reference Batoz JL, Bathe KJ, Ho LW (1980) A study of three-node triangular plate bending element. Int J Numer Methods Eng 15:1771–1812CrossRefMATH Batoz JL, Bathe KJ, Ho LW (1980) A study of three-node triangular plate bending element. Int J Numer Methods Eng 15:1771–1812CrossRefMATH
32.
go back to reference Katili I (1993) A new discrete Kirchhoff–Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—part I: an extended DKT element for thick-plate bending analysis. Int J Numer Methods Eng 36:1859–1883CrossRefMATH Katili I (1993) A new discrete Kirchhoff–Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—part I: an extended DKT element for thick-plate bending analysis. Int J Numer Methods Eng 36:1859–1883CrossRefMATH
33.
go back to reference Chen W, Cheung YK (2001) Refined 9-Dof triangular Mindlin plate elements. Int J Numer Methods Eng 51:1259–1281CrossRefMATH Chen W, Cheung YK (2001) Refined 9-Dof triangular Mindlin plate elements. Int J Numer Methods Eng 51:1259–1281CrossRefMATH
34.
go back to reference Zienkiewicz OC, Lefebvre D (1988) A robust triangular plate bending element of the Reissner–Mindlin type. Int J Numer Methods Eng 26:1169–1184CrossRefMATH Zienkiewicz OC, Lefebvre D (1988) A robust triangular plate bending element of the Reissner–Mindlin type. Int J Numer Methods Eng 26:1169–1184CrossRefMATH
35.
go back to reference Sze KY, Zhu D, Chen DP (1997) Quadratic triangular C0 plate bending element. Int J Numer Methods Eng 40:937–951CrossRefMATH Sze KY, Zhu D, Chen DP (1997) Quadratic triangular C0 plate bending element. Int J Numer Methods Eng 40:937–951CrossRefMATH
36.
go back to reference Bathe KJ, Brezzi F, Cho SW (1989) The MITC7 and MITC9 plate bending element. Comput Struct 32:797–814CrossRefMATH Bathe KJ, Brezzi F, Cho SW (1989) The MITC7 and MITC9 plate bending element. Comput Struct 32:797–814CrossRefMATH
37.
go back to reference Batoz JL, Tahar MB (1982) Evaluation of a new quadrilateral thin plate bending element. Int J Numer Methods Eng 18:1655–1677CrossRefMATH Batoz JL, Tahar MB (1982) Evaluation of a new quadrilateral thin plate bending element. Int J Numer Methods Eng 18:1655–1677CrossRefMATH
38.
go back to reference Katili I (1993) A new discrete Kirchhoff–Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—Part II: an extended DKQ element for thick-plate bending analysis. Int J Numer Methods Eng 36:1885–1908CrossRefMATH Katili I (1993) A new discrete Kirchhoff–Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—Part II: an extended DKQ element for thick-plate bending analysis. Int J Numer Methods Eng 36:1885–1908CrossRefMATH
39.
go back to reference Sofuoglu H, Gedikli H (2007) A refined 5-node plate bending element based on Reissner–Mindlin theory. Commun Numer Methods Eng 23:385–403CrossRefMATH Sofuoglu H, Gedikli H (2007) A refined 5-node plate bending element based on Reissner–Mindlin theory. Commun Numer Methods Eng 23:385–403CrossRefMATH
40.
go back to reference Zienkiewicz OC, Cheung YK (1964) The finite element method for analysis of elastic isotropic and orthotropic slabs. Proc Inst Civ Eng 28:471–488 Zienkiewicz OC, Cheung YK (1964) The finite element method for analysis of elastic isotropic and orthotropic slabs. Proc Inst Civ Eng 28:471–488
41.
go back to reference Malkus DS, Hughes TJR (1978) Mixed finite element methods-reduced and selective integration techniques: a unification of concepts. Comput Methods Appl Mech Eng 15:63–81ADSCrossRefMATH Malkus DS, Hughes TJR (1978) Mixed finite element methods-reduced and selective integration techniques: a unification of concepts. Comput Methods Appl Mech Eng 15:63–81ADSCrossRefMATH
42.
go back to reference Zienkiewicz OC, Xu Z, Ling FZ, Samuelsson A, Wiberg NE (1993) Linked interpolation for Reissner–Mindlin plate element: part I—a simple quadrilateral. Int J Numer Methods Eng 36:3043–3056CrossRefMATH Zienkiewicz OC, Xu Z, Ling FZ, Samuelsson A, Wiberg NE (1993) Linked interpolation for Reissner–Mindlin plate element: part I—a simple quadrilateral. Int J Numer Methods Eng 36:3043–3056CrossRefMATH
43.
go back to reference Bathe KJ, Dvorkin EH (1985) A four-node plate bending element based on Mindlin–Reissner plate theory and mixed interpolation. Int J Numer Methods Eng 21:367–383CrossRefMATH Bathe KJ, Dvorkin EH (1985) A four-node plate bending element based on Mindlin–Reissner plate theory and mixed interpolation. Int J Numer Methods Eng 21:367–383CrossRefMATH
44.
go back to reference Soh AK, Cen S, Long YQ, Long ZF (2001) A new twelve DOF quadrilateral element for analysis of thick and thin plates. Eur J Mech A Solids 20:299–326MathSciNetCrossRefMATH Soh AK, Cen S, Long YQ, Long ZF (2001) A new twelve DOF quadrilateral element for analysis of thick and thin plates. Eur J Mech A Solids 20:299–326MathSciNetCrossRefMATH
45.
go back to reference Tocher JL, Kapur KK (1965) Basis of derivation of matrices for direct stiffness method. AIAA J 3(6):1215–1216ADSCrossRef Tocher JL, Kapur KK (1965) Basis of derivation of matrices for direct stiffness method. AIAA J 3(6):1215–1216ADSCrossRef
46.
go back to reference Shin CM, Lee BC (2014) Development of a strain-smoothed three-node triangular flat shell element with drilling degrees of freedom. Finite Elem Anal Des 86:71–80MathSciNetCrossRef Shin CM, Lee BC (2014) Development of a strain-smoothed three-node triangular flat shell element with drilling degrees of freedom. Finite Elem Anal Des 86:71–80MathSciNetCrossRef
47.
go back to reference Wang C, Hu P, Xia Y (2012) A 4-node quasi-conforming Reissner–Mindlin shell element by using Timoshenko’s beam function. Finite Elem Anal Des 61:12–22MathSciNetCrossRef Wang C, Hu P, Xia Y (2012) A 4-node quasi-conforming Reissner–Mindlin shell element by using Timoshenko’s beam function. Finite Elem Anal Des 61:12–22MathSciNetCrossRef
48.
go back to reference Norachan P, Suthasupradit S, Kim KD (2012) A co-rotational 8-node degenerated thin-walled element with assumed natural strain and enhanced assumed strain. Finite Elem Anal Des 50:70–85MathSciNetCrossRef Norachan P, Suthasupradit S, Kim KD (2012) A co-rotational 8-node degenerated thin-walled element with assumed natural strain and enhanced assumed strain. Finite Elem Anal Des 50:70–85MathSciNetCrossRef
49.
go back to reference Mostafa M, Sivaselvan MV, Felippa CA (2013) A solid-shell corotational element based on ANDES, ANS and EAS for geometrically nonlinear structural analysis. Int J Numer Methods Eng 95:145–180MathSciNetCrossRefMATH Mostafa M, Sivaselvan MV, Felippa CA (2013) A solid-shell corotational element based on ANDES, ANS and EAS for geometrically nonlinear structural analysis. Int J Numer Methods Eng 95:145–180MathSciNetCrossRefMATH
50.
go back to reference Felippa CA, Alexander S (1992) Membrane triangles with corner drilling freedoms: III. Implementation and performance evaluation. Finite Elem Anal Des 12:203–239CrossRefMATH Felippa CA, Alexander S (1992) Membrane triangles with corner drilling freedoms: III. Implementation and performance evaluation. Finite Elem Anal Des 12:203–239CrossRefMATH
51.
go back to reference Bergan PG, Felippa CA (1985) A triangular membrane element with rotational degrees of freedom. Comput Methods Appl Mech Eng 50:25–69ADSCrossRefMATH Bergan PG, Felippa CA (1985) A triangular membrane element with rotational degrees of freedom. Comput Methods Appl Mech Eng 50:25–69ADSCrossRefMATH
52.
go back to reference Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-Hill, New YorkMATH Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-Hill, New YorkMATH
53.
go back to reference Morley LSD (1963) Skew plates and structures. Pergamon Press, OxfordMATH Morley LSD (1963) Skew plates and structures. Pergamon Press, OxfordMATH
54.
go back to reference Razzaque A (1973) Program for triangular bending elements with derivative smoothing. Int J Numer Methods Eng 6:333–345CrossRef Razzaque A (1973) Program for triangular bending elements with derivative smoothing. Int J Numer Methods Eng 6:333–345CrossRef
55.
go back to reference Reissner E, Stein M (1951) Torsion and transverse bending of cantilever plates, Technical Note 2369, NACA, Washington DC Reissner E, Stein M (1951) Torsion and transverse bending of cantilever plates, Technical Note 2369, NACA, Washington DC
57.
go back to reference Macneal RH, Harder RL (1985) A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Des 1(1):3–20CrossRef Macneal RH, Harder RL (1985) A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Des 1(1):3–20CrossRef
Metadata
Title
An efficient flat shell element
Authors
Mohammad Rezaiee-Pajand
Majid Yaghoobi
Publication date
13-10-2017
Publisher
Springer Netherlands
Published in
Meccanica / Issue 4-5/2018
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-017-0772-4

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