Inflectional Heavy Elastica with Unilateral Contact constraint: Analytical Solution through the Curvilinear Abscissa Mapping approximation

Iandiorio, Christian; Salvini, P

doi:10.1016/j.ijsolstr.2021.111258

Cited by 3 publications

(6 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The boundary conditions in (11) form a boundary value problem. An interesting physical interpretation of the Lagrangian multiplier λ is evident if the first of the equations ( 9) is compared with the general equation that governs the large displacement of beams [31].…”

Section: The 6th International Conference On Numerical Modelling In E...mentioning

confidence: 99%

“…Thin-walled structures are easily subjected to high deformations due to mechanical and thermal loads; therefore, they require a more accurate insight regarding phenomena that would be neglected in more massive structures [5,6]. Considering the danger connected to failure, it is crucial to study how the operational or exceptional loads (e.g., pipelines installations [7][8][9][10][11][12][13][14]) affect structural integrity and reliability. Among the various scenarios that can affect this type of structures, for thin-walled pipes, it is worthwhile to consider the ovalization due to bending, i.e., the in-plane warping of the sections (figures 1 and 2).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bending Ovalization of Thin-Walled Circular Tubes

Iandiorio,

Salvini

2024

Advances in Science and Technology

Self Cite

View full text Add to dashboard Cite

This paper presents a new analytical model to predict the mechanical behaviour of an elastic straight thin-walled circular tube (pipe) subjected to bending. A thin-walled pipe cannot be modelled as a simple beam, inasmuch it presents a shell-like behaviour due to the ovalization (in-plane warping) of the cross-section when loaded. The section modification implies a non-linear trend between the applied moment and the axial curvature, i.e. a non-invariance of the section moment of inertia. Two analytical ways are proposed in the reference literature: a rigorous one due to Reissner use a stress-function approach, and an approximated one, first due to Brazier, that follows Ritz approach. The Reissner model is analytically unsolvable and difficult to face numerically due to some integral conditions to fulfill. On the contrary, the Ritz approach is easy to implement, but being Heuristic is limited to circular sections. To overcome the previous mentioned difficulties a new geometrically exact Pipe model in terms of displacements is proposed, which turns out to be a mix between a shell and a beam model. The present approach leads to a system of ODEs accompanied by Boundary Value Problems (not requiring any integral conditions) that can be solved using a direct collocation method. After solving it, we build-up the dimensionless (non-linear) moment-curvature diagram, valid for any straight pipe, i.e. for every diameter, thickness, and whatever linear elastic material. The results are compared with other literature solutions performed using the Ritz’s approach and with Finite Element Analysis.

show abstract

Section: The 6th International Conference On Numerical Modelling In E...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bending Ovalization of Thin-Walled Circular Tubes

Iandiorio,

Salvini

2024

Advances in Science and Technology

Self Cite

View full text Add to dashboard Cite

show abstract

“…Equations ( 33)-( 35) form a nonlinear first-order ODE system that holds for every type of flexure hinge (with variable section, initially curvilinear, etc.). It is not possible to solve this analytically in a general form (i.e., for all types of load conditions) [37,39,54]. The boundary conditions (b.c.)…”

Section: A Comprehensive Analytical Model Of Flexure Hinge Kinematicsmentioning

confidence: 99%

“…As is well known, the numerical methods employed to solve ODE only work with initial value problems (i.v.p. ); therefore, to solve a b.v.p., a shooting method should be adopted [37,39] that involves integrating the systems of Equations ( 33)-( 35) several times.…”

Section: A Comprehensive Analytical Model Of Flexure Hinge Kinematicsmentioning

confidence: 99%

See 1 more Smart Citation

Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

Iandiorio

Salvini

2023

Micromachines

Self Cite

View full text Add to dashboard Cite

The kinematic synthesis of compliant mechanisms based on flexure hinges is not an easy task. A commonly used method is the equivalent rigid model, which involves replacing the flexure hinges with rigid bars connected with lumped hinges using the already known methods of synthesis. This way, albeit simpler, hides some interesting issues. This paper addresses the elasto-kinematics and instantaneous invariants of flexure hinges with a direct approach, making use of a nonlinear model to predict their behaviour. The differential equations that govern the nonlinear geometric response are given in a comprehensive form and are solved for flexure hinges with constant sections. The solution to the nonlinear model is then used to obtain an analytical description of two instantaneous invariants: the centre of instantaneous rotation (c.i.r.) and the inflection circle. The main result is that the c.i.r. evolution, namely the fixed polode, is not conservative but is loading-path dependent. Consequently, all other instantaneous invariants are loading-path dependent, and the property of instantaneous geometric invariants (independent of the motion time law) can no longer be used. This result is analytically and numerically evidenced. In other words, it is shown that a careful kinematic synthesis of compliant mechanisms cannot be addressed by only considering the kinematics as rigid mechanisms, and it is essential to take into consideration the applied loads and their histories.

show abstract

Updated Lagrangian Curvilinear Beam Element for 2D Large Displacement Analysis

Iandiorio

Salvini

2023

Lecture Notes in Mechanical Engineering

View full text Add to dashboard Cite

Inflectional Heavy Elastica with Unilateral Contact constraint: Analytical Solution through the Curvilinear Abscissa Mapping approximation

Cited by 3 publications

References 26 publications

Bending Ovalization of Thin-Walled Circular Tubes

Bending Ovalization of Thin-Walled Circular Tubes

Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

Updated Lagrangian Curvilinear Beam Element for 2D Large Displacement Analysis

Contact Info

Product

Resources

About