Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

Tullini, Nerio; Tralli, Antonio

doi:10.1007/s00466-009-0431-2

Cited by 19 publications

(54 citation statements)

References 43 publications

(70 reference statements)

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“…Using the theorem of work and energy for exterior domains, it may be demonstrated that the total potential energy for the substrate, ∏ soil , is given by (Tullini and Tralli, 2010;Tullini et al, 2012):…”

Section: Total Potential Energy For the Substratementioning

confidence: 99%

“…In this study, the shape functions collected by matrix N a (ξ) = [N a,1 , N a,2 ] are linear Lagrangian polynomials N a,1 1-ξ and N a,2 = ξ, whereas matrix N b (ξ) assembles the "modified" Hermitian shape functions already adopted by Minghini et al (2009;2010;Tullini and Tralli, 2010;Tullini et al, 2013b).…”

Section: Finite Element Modelmentioning

confidence: 99%

“…For a structure connected to a foundation beam, Equation 14 can be partitioned as reported by Tullini and Tralli (2010;Tullini et al, 2012). In particular, denoting with q 1 and q 2 the vectors of nodal displacements referred to the structure only and those shared between structure and foundation beam, respectively and with f 1 and f 2 the corresponding load vectors, Equation (14) takes the form:…”

Section: Finite Element Modelmentioning

confidence: 99%

“…For example, Tullini et al (2012) used quadratic Lagrangian bar elements including one or two equal substrate elements, whereas Tullini and Tralli (2010) used beam-substrate matrices obtained adopting four equal soil elements for each beam element.…”

Section: Prismatic Beam With Piecewise Constant Surface Tractionsmentioning

confidence: 99%

“…Therefore, the independent variables of the proposed formulation are beam nodal displacements and rotations and soil tangential and normal surface tractions. An analogous formulation was used by Tullini and Tralli (2010;Tullini et al., 2012) for the analysis of Timoshenko beams in frictionless contact with the substrate and of bars and thin coatings (i.e., mono-dimensional elements without bending stiffness), respectively. The same mixed model was used by Tullini et al (2013a;2013b) for the analysis of elastic instability of beams and frames in frictionless contact with the substrate.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Nonlinear Analysis of RC Box Culverts Resting on a Linear Elastic Soil

Baraldi¹,

Minghini²,

Tezzon³

et al. 2018

International Journal of Structural Glass and Advanced Material

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In the analyses presented, the soil-structure interaction is accounted for by means of a FE-BIE approach, in which the structure is modelled with displacement-based beam finite elements, whereas the boundary between structure and substrate is described in terms of surface tractions by means of a boundary integral equation incorporating a suitable Green's function. This mixed formulation ensures full continuity between structure and substrate in terms of displacements and rotations. To take account of structural nonlinearities, potential plastic hinges are defined at the end sections of the beam elements in the form of semi-rigid connections characterized by a rigidplastic moment-rotation relationship. The incremental analyses carried out emphasize the effectiveness of the model in reproducing collapse mechanisms and stiffness loss of the structure for increasing loads. Moreover, the adopted formulation is able to capture both interfacial shear tractions and vertical normal tractions which develop along the substrate boundary under a variety of loading conditions.

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Section: Total Potential Energy For the Substratementioning

confidence: 99%

Section: Finite Element Modelmentioning

confidence: 99%

Section: Finite Element Modelmentioning

confidence: 99%

Section: Prismatic Beam With Piecewise Constant Surface Tractionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear Analysis of RC Box Culverts Resting on a Linear Elastic Soil

Baraldi¹,

Minghini²,

Tezzon³

et al. 2018

International Journal of Structural Glass and Advanced Material

Self Cite

View full text Add to dashboard Cite

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Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation

Sapountzakis

Kampitsis

2011

Arch Appl Mech

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In this paper, a boundary element method is developed for the nonlinear analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross-section, partially supported on tensionless three-parameter foundation, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM-based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples are worked out to illustrate the efficiency, wherever possible, the accuracy and the range of applications of the developed method.

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Stability of slender beams and frames resting on 2D elastic half-space

2012

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Making use of a mixed variational formulation based on the Green function of the substrate, which assumes as independent fields the structure displacements and the contact pressure, a simple and efficient Finite Element-Boundary Integral Equation (FE-BIE) coupling method is derived and applied to the stability analysis of beams and frames resting on an elastic half-plane. Slender Euler-Bernoulli beams with different combinations of end constraints are considered. The examples illustrate the convergence to the existing exact solutions and provide new estimates of the buckling loads for different boundary conditions. Finally, nonlinear incremental analyses of rectangular pipes with compressed columns and free or pinned foundation ends are performed, showing that pipes stiffer than the soil may exhibit snapthrough instability

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Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

Cited by 19 publications

References 43 publications

Nonlinear Analysis of RC Box Culverts Resting on a Linear Elastic Soil

Nonlinear Analysis of RC Box Culverts Resting on a Linear Elastic Soil

Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation

Stability of slender beams and frames resting on 2D elastic half-space

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