A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling
From MaRDI portal
Publication:5243038
DOI10.1177/1081286517737000zbMath1425.74267OpenAlexW2790110885MaRDI QIDQ5243038
Mario Spagnuolo, Ugo A. Andreaus
Publication date: 13 November 2019
Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)
Full work available at URL: http://journals.sagepub.com/doi/abs/10.1177/1081286517737000?journalCode=mmsa
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Bifurcation and buckling (74G60) Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids (74-02)
Related Items (21)
A numerical method for inextensible elastic filaments in viscous fluids ⋮ Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory ⋮ Rules governing swarm robot in continuum mechanics ⋮ An updated Lagrangian Bézier finite element formulation for the analysis of slender beams ⋮ Fluid diffusion related aging effect in a concrete dam modeled as a Timoshenko beam ⋮ Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations ⋮ On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure ⋮ Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences ⋮ Variational asymptotic homogenization of beam-like square lattice structures ⋮ Nonlinear vibration, stability, and bifurcation analysis of unbalanced spinning pre-twisted beam ⋮ A discrete formulation of Kirchhoff rods in large-motion dynamics ⋮ A non-linear symmetric \(\mathrm{G}^1\)-conforming Bézier finite element formulation for the analysis of Kirchhoff beam assemblies ⋮ Energy-based trajectory tracking and vibration control for multilink highly flexible manipulators ⋮ Three-point bending test of pantographic blocks: numerical and experimental investigation ⋮ The Effect of Mechanical Load-induced Intraosseous Pressure Gradients on Bone Remodeling ⋮ Analytical Solutions of 2-dimensional Second Gradient Linear Elasticity for Continua with Cubic-D4 Microstructure ⋮ How the Properties of Pantographic Elementary Lattices Determine the Properties of Pantographic Metamaterials ⋮ On boundary layers observed in some 1D second-gradient theories ⋮ From the swarm robotics to material deformations ⋮ Pantographic beam: a complete second gradient 1D-continuum in plane ⋮ Finite element formulations for constrained spatial nonlinear beam theories
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the whole spectrum of Timoshenko beams. II: Further applications
- Simplified analysis of a generalized bias test for fabrics with two families of inextensible fibres
- Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches
- Dynamics of taut strings traveled by train of forces
- Comment to ``Hypertractions and hyperstresses convey the same mechanical information`` by Prof. Podio-Guidugli and Prof. Vianello and some related papers on higher gradient theories
- Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method
- Elliptic integral solution of the extensible elastica with a variable length under a concentrated force
- Vibration analysis of non-linear 6-parameter prestressed shells
- Stability of inflectional elasticae centered at vertices or inflection points
- A second gradient formulation for a 2D fabric sheet with inextensible fibres
- A review on 2D models for the description of pantographic fabrics
- Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models
- An explicit solution for the dynamics of a taut string of finite length carrying a traveling mass: the subsonic case
- Advanced methods of continuum mechanics for materials and structures
- Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches
- Buckling and post-buckling of extensible rods revisited: a multiple-scale solution
- Isogeometric sizing and shape optimisation of beam structures
- The variational structure of a nonlinear theory for spatial lattices
- Stability of nonlinearly elastic rods
- An explicit, totally analytic approximate solution for Blasius' viscous flow problems
- Large deflections of cantilever beams of non-linear elastic material under a combined loading
- Complete solution of the stability problem for elastica of Euler's column
- Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof
- Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence
- Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads
- A new technique for large deflection analysis of non-prismatic cantilever beams
- On the bending of viscoelastic plates made of polymer foams
- Controllable deformations of elastic spatial rods
- Variational theory for spatial rods
- On the nonlinear mechanics of discrete networks
- A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium
- Advances in the mechanics of plates and shells. The Avinoam Libai anniversary volume.
- Determination of the closure of the set of elasticity functionals
- A further study on the postbuckling of extensible elastic rods
- Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices
- Statics of shallow inclined elastic cables under general vertical loads: a perturbation approach
- On the shell theory on the nanoscale with surface stresses
- Improved numerical integration for locking treatment in isogeometric structural elements. I: Beams
- Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model
- How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert
- Sufficient conditions for stability of Euler elasticas
- Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends
- Nonlinear dynamics of filaments. II: Nonlinear analysis
- Nonlinear dynamics of filaments. I: Dynamical instabilities
- A two-dimensional gradient-elasticity theory for woven fabrics
- On generalized Cosserat-type theories of plates and shells: a short review and bibliography
- A continuum mechanics based derivation of Reissner's large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli-Euler beams
- Extensional \textit{Elastica} in large deformation as \(\Gamma \)-limit of a discrete 1D mechanical system
- Exact solutions for the buckling and postbuckling of shear-deformable beams
- A revisitation of the paradox of discontinuous trajectory for a mass particle moving on a taut string
- Large deformation and stability of an extensible elastica with an unknown length
- Buckling and post-buckling analysis of extensible beam-columns by using the differential quadrature method
- Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations
- An explicit solution of the large deformation of a cantilever beam under point load at the free tip
- Positive solutions for a nonlinear Kirchhoff type beam equation
- Non-linear bending of beams with uniformly distributed loads
- On one-dimensional finite-strain beam theory: the plane problem
- Consistent tangent operator for an exact Kirchhoff rod model
- Non-local interactions resulting from the homogenization of a linear diffusive medium
- Boundary stabilization for a non-linear beam on elastic bearings
- Constitutive models for strongly curved beams in the frame of isogeometric analysis
- A complete dynamic approach to the Generalized Beam Theory cross-section analysis including extension and shear modes
- Hencky Bar-Chain Model for Buckling and Vibration of Beams with Elastic End Restraints
- On constitutive inequalities in nonlinear theory of elastic shells
- Semigroup model and stability of the structurally damped Timoshenko beam with boundary inputs
- Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
- CLASSIFICATION OF THE SPATIAL EQUILIBRIA OF THE CLAMPED ELASTICA: NUMERICAL CONTINUATION OF THE SOLUTION SET
- CLOSURE OF THE SET OF DIFFUSION FUNCTIONALS WITH RESPECT TO THE MOSCO-CONVERGENCE
- Existence of solutions for fourth order elliptic equations of Kirchhoff type on RN
- Geometric conditions for the positive definiteness of the second variation in one-dimensional problems
- STEADY STATES OF THE HINGED EXTENSIBLE BEAM WITH EXTERNAL LOAD
- Isogeometric analysis of plane-curved beams
- Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives
- The Rayleigh and Courant variational principles in the six-parameter shell theory
- At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola
- Behaviour of the extensible elastical solution
This page was built for publication: A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling