The analysis of beams on layered poroelastic soils with anisotropic permeability and compressible pore fluid. (English) Zbl 1465.74119
Summary: The stiffness matrices of the Euler-Bernoulli/Timoshenko beams are established based on the finite element method (FEM), while the solution of layered poroelastic soils with anisotropic permeability and compressible pore fluid is obtained with the analytical layer-element method. Then by introducing the conditions of the displacement harmony between the beams and foundation, we can establish the final stiffness matrices of foundation beams. Three examples are conducted to compare the results of the proposed theory with those from the literatures or the ABAQUS modeling in order to prove the accuracy of the theory. Furthermore, several other numerical examples are carried out to analyze the effects of the property of the beam-soil system and the shear deformation and rotary inertia on the interaction problems.
MSC:
| 74L10 | Soil and rock mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
Euler-Bernoulli/Timoshenko beams; layered poroelastic soils; anisotropic permeability; compressible pore fluid; finite element method (FEM); analytical layer-element methodSoftware:
ABAQUSReferences:
| [1] | Hetényi, M., Beams on Elastic Foundations (1946), University of Michigan Press: University of Michigan Press Ann Arbor, Michigan · Zbl 0218.73070 |
| [2] | Kaschiev, M. S.; Mikhajlov, K., A beam resting on a tensionless Winkler foundation, Comput. Struct., 55, 2, 261-264 (1995) · Zbl 0900.73268 |
| [3] | Ioakimidis, N. I., Inequality constrains in one-dimensional finite elements for an elastic beam on a tensionless Winkler foundation, Finite Elem. Anal. Des., 24, 2, 67-75 (1996) · Zbl 0875.73332 |
| [4] | Zhao, H. F.; Cooker, R. D., Beam element on two-parameter elastic foundations, J. Eng. Mech., 109, 6, 1390-1402 (1983) |
| [5] | Celep, Z.; Demir, F., Symmetrically loaded beam on a two-parameter tensionless foundation, Struct. Eng. Mech., 27, 5, 555-574 (2007) |
| [6] | Basu, D.; Kameswara Rao, N. S.V., Analytical solutions for Euler-Bernoulli beam on viscoelastic foundation subjected to moving load, Int. J. Numer. Anal. Methods Geomech., 37, 8, 945-960 (2013) |
| [7] | Selvadurai, A. P.S., Elastic Analysis of Soil-Foundation interaction (1979), Elsevier Scientific Publishing Company: Elsevier Scientific Publishing Company New York |
| [8] | Ai, Z. Y.; Li, Z. X.; Cheng, Y. C., BEM analysis of elastic foundation beams on multilayered isotropic soils, Soils Found., 54, 4, 667-674 (2014) |
| [9] | Timoshenko, S. P., On the correction for shear of the differential equation for transverse vibration of prismatic bars, Philos. Mag., 41, 245, 744-746 (1921) |
| [10] | Timoshenko, P. S., On the transverse vibrations of bars of uniform cross-section, Philos. Mag., 43, 253, 125-131 (1922) |
| [11] | Levinson, M., A new rectangular beam theory, J. Sound Vib., 74, 1, 81-87 (1981) · Zbl 0453.73058 |
| [12] | Bickford, W. B., A consistent higher order beam theory, Dev. Theor. Appl. Mech., 11, 137-150 (1982) |
| [13] | Shimpi, R. C., Zeroth order shear deformation theory for plates, AIAA J., 37, 4, 524-526 (1999) |
| [14] | Auricchio, F.; Sacco, E., Refined first-order shear deformation theory models for composite laminates, J. Appl. Mech., 70, 3, 381-390 (2003) · Zbl 1110.74320 |
| [15] | Pavan Kumar, D. V.T. G.; Raghu Prasad, B. K., Higher-order beam theories for mode II fracture of unidirectional composites, J. Appl. Mech., 70, 6, 840-852 (2003) · Zbl 1110.74521 |
| [16] | Chen, G. J., Consolidation of multilayered half space with anisotropic permeability and compressible constituents, Int. J. Solids Struct., 41, 16, 4567-4586 (2004) · Zbl 1133.74310 |
| [17] | Ai, Z. Y.; Zeng, W. Z., Consolidation analysis of saturated multi-layered soils with anisotropic permeability caused by a point sink, Int. J. Numer. Anal. Methods Geomech., 37, 7, 758-770 (2013) |
| [18] | Sneddon, I. N., The Use of Integral Transform (1972), McGraw-Hill: McGraw-Hill New York · Zbl 0237.44001 |
| [19] | Ai, Z. Y.; Yue, Z. Q.; Tham, L. G.; Yang, M., Extended Sneddon and Muki solutions for multilayered elastic materials, Int. J. Eng. Sci., 40, 13, 1453-1483 (2002) · Zbl 1211.74105 |
| [20] | Talbot, A., The accurate numerical inversion of Laplace transforms, IMA J. Appl. Math., 23, 1, 97-120 (1979) · Zbl 0406.65054 |
| [21] | Booker, J. R.; Small, J. C., A method of computing the consolidation behavior of layered soils using direct numerical inversion of Laplace transforms, Int. J. Numer. Anal. Methods Geomech., 11, 4, 363-380 (1987) · Zbl 0612.73109 |
| [23] | Ganbe, T.; Kurashige, M., Integral equations for a 3D crack in a fluid saturated poroelastic infinite space of transversely isotropic permeability, JSME Int. J. Ser. A, 44, 3, 423-430 (2001) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
