A torsional spring-like beam element for the dynamic analysis of flexible multibody systems. (English) Zbl 0879.73076
The author considers the large displacement and large rigid-body motion of systems of linkages, the elements of which may also undergo bending and axial deformations. Dynamic conditions are assumed. The main aim is to develop a beam finite element which does not make use of slope degrees of freedom. This is achieved by treating a typical beam as a composite element comprising two subelements which model axial and bending response, respectively.
A convected frame of reference is chosen for the description of element behaviour; this frame translates and rotates with the element, while remaining rectilinear. The beam element consists of two linked truss elements, whose behaviour is further determined by a spring-like bending element attached to the two truss elements. The beam shape is given by a cubic polynomial, and the information is sufficient to determine the form of this cubic in terms of the truss element geometry. The strain energy of the composite element may be written explicitly in terms of the material and geometrical properties of the element. Force-displacement relations can then be easily derived, together with the stiffness matrix. The formulation of the discrete problem is completed by introducing the Newmark scheme for time integration.
Two examples are treated: a high-speed flexible four-bar linkage, and a highly flexible rotating beam. In the first example, numerical results are compared with those obtained experimentally, while in the second example the results are compared with those obtained numerically. In both cases, the results compared show good aggreement.
A convected frame of reference is chosen for the description of element behaviour; this frame translates and rotates with the element, while remaining rectilinear. The beam element consists of two linked truss elements, whose behaviour is further determined by a spring-like bending element attached to the two truss elements. The beam shape is given by a cubic polynomial, and the information is sufficient to determine the form of this cubic in terms of the truss element geometry. The strain energy of the composite element may be written explicitly in terms of the material and geometrical properties of the element. Force-displacement relations can then be easily derived, together with the stiffness matrix. The formulation of the discrete problem is completed by introducing the Newmark scheme for time integration.
Two examples are treated: a high-speed flexible four-bar linkage, and a highly flexible rotating beam. In the first example, numerical results are compared with those obtained experimentally, while in the second example the results are compared with those obtained numerically. In both cases, the results compared show good aggreement.
Reviewer: B.D.Reddy (Rondebosch)
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
Keywords:
force-displacement relations; large displacement; large rigid-body motion; bending; axial deformations; convected frame of reference; two linked truss elements; cubic polynomial; strain energy; stiffness matrix; Newmark scheme; time integration; high-speed flexible four-bar linkage; highly flexible rotating beamReferences:
| [1] | Christensen, Comput. Struct. 23 pp 819– (1986) · Zbl 0589.73059 · doi:10.1016/0045-7949(86)90251-8 |
| [2] | Yigit, J. Sound Vib. 121 pp 201– (1988) · Zbl 1235.74203 · doi:10.1016/S0022-460X(88)80024-5 |
| [3] | Bakr, Comput. Struct. 23 pp 739– (1986) · Zbl 0589.73060 · doi:10.1016/0045-7949(86)90242-7 |
| [4] | Naganathan, Int. J. Robotics Res. 6 pp 75– (1987) · doi:10.1177/027836498700600106 |
| [5] | Wu, Int. J. numer. methods eng. 26 pp 2211– (1988) · Zbl 0661.73059 · doi:10.1002/nme.1620261006 |
| [6] | Ider, J. Appl. Mech. 56 pp 444– (1989) · Zbl 0711.73137 · doi:10.1115/1.3176103 |
| [7] | Gordaninejad, J. Vib. Acoustic 113 pp 461– (1991) · doi:10.1115/1.2930208 |
| [8] | Yang, J. Mech. Des. 112 pp 175– (1990) · doi:10.1115/1.2912590 |
| [9] | Boutaghou, Comput. Struct. 38 pp 605– (1991) · Zbl 0825.73710 · doi:10.1016/0045-7949(91)90012-B |
| [10] | Boutaghou, J. Vib. Acoustics 113 pp 495– (1991) · doi:10.1115/1.2930213 |
| [11] | Boutaghou, J. Appl. Mech. 59 pp 991– (1992) · Zbl 0770.73041 · doi:10.1115/1.2894071 |
| [12] | Kane, J. Guidance Control Dyn. 10 pp 139– (1987) · doi:10.2514/3.20195 |
| [13] | Liou, Vib. Acoustics Stress Reliability Des. 111 pp 35– (1989) · doi:10.1115/1.3269820 |
| [14] | Banerjee, J. Guidance Control Dyn. 13 pp 221– (1990) · doi:10.2514/3.20540 |
| [15] | Jablokow, J. Mech. Des. 115 pp 314– (1993) · doi:10.1115/1.2919194 |
| [16] | Buffinton, J. Dyn. Systems Measurement Control 114 pp 41– (1992) · Zbl 0775.93144 · doi:10.1115/1.2896506 |
| [17] | Friberg, Int. J. numer. methods eng. 32 pp 1637– (1991) · doi:10.1002/nme.1620320808 |
| [18] | Book, Int. J. Robotics Res. 3 pp 87– (1984) · doi:10.1177/027836498400300305 |
| [19] | Khulief, Comput. Methods Appl. Mech. Eng. 97 pp 23– (1992) · Zbl 0775.73266 · doi:10.1016/0045-7825(92)90105-S |
| [20] | Wright, J. Appl. Mech. 49 pp 197– (1982) · Zbl 0482.73041 · doi:10.1115/1.3161966 |
| [21] | Belytschko, Int. J. numer. methods eng. 7 pp 255– (1973) · Zbl 0265.73062 · doi:10.1002/nme.1620070304 |
| [22] | Belytschko, Int. J. numer. methods eng. 11 pp 65– (1977) · Zbl 0347.73053 · doi:10.1002/nme.1620110108 |
| [23] | Argyris, Comput. Methods Appl. Mech. Eng. 17/18 pp 1– (1979) · Zbl 0407.73058 · doi:10.1016/0045-7825(79)90083-5 |
| [24] | Rankin, J. Pressure Vessel Technol. 108 pp 165– (1986) · doi:10.1115/1.3264765 |
| [25] | Rankin, Comput. Struct. 30 pp 257– (1988) · Zbl 0668.73054 · doi:10.1016/0045-7949(88)90231-3 |
| [26] | Simo, J. Appl. Mech. 53 pp 849– (1986) · Zbl 0607.73057 · doi:10.1115/1.3171870 |
| [27] | Simo, Int. J. Solids Struct. 27 pp 371– (1991) · Zbl 0731.73029 · doi:10.1016/0020-7683(91)90089-X |
| [28] | Cardona, Int. J. numer. methods eng. 26 pp 2403– (1988) · Zbl 0662.73049 · doi:10.1002/nme.1620261105 |
| [29] | Cardona, Int. J. numer. methods eng. 32 pp 1565– (1991) · Zbl 0825.73349 · doi:10.1002/nme.1620320805 |
| [30] | Park, Int. J. numer. methods eng. 32 pp 1767– (1991) · Zbl 0779.73036 · doi:10.1002/nme.1620320815 |
| [31] | Downer, Comput. Methods Appl. Mech. Eng. 96 pp 373– (1992) · Zbl 0764.73045 · doi:10.1016/0045-7825(92)90072-R |
| [32] | and , The Finite Element Method 4th edn, McGraw-Hill, New York, 1989. |
| [33] | Strength of Materials, 3rd edn, D. Van Nostrand Company, Princeton, N.J., 1956. |
| [34] | and , ’Dynamics strains in a four bar mechanism’, Proc. 3rd Applied Mechanism Conf., Stillwaterm Okla, Paper No. 26, 1973. |
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