Theoretical and experimental analysis of the von Mises truss subjected to a horizontal load using a new hyperelastic model with hardening

Pelliciari, Matteo; Falope, Federico Oyedeji; Lanzoni, Luca; Tarantino, Angelo Marcello

doi:10.1016/j.euromechsol.2022.104825

Cited by 5 publications

(1 citation statement)

References 44 publications

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“…The material law is the helical Cauchy-Born rule. Interesting results are related to the stability problem of the von Mises truss in [14] by taking into account the geometric and material nonlinearity and the shear deformation as well.…”

Section: Introductionmentioning

confidence: 99%

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

2023

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It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated with homogeneous boundary conditions—the mentioned BVPs constitute three eigenvalue problems. They are solved by using a novel solution strategy based on the Green functions that belong to these BVPs: the eigenvalue problems established for the critical load are transformed into eigenvalue problems governed by homogeneous Fredholm integral equations with kernels that can be given in closed forms provided that the Green function of each BVP is known. Then the eigenvalue problems governed by the Fredholm integral equations can be manipulated into algebraic eigenvalue problems solved numerically by using effective algorithms. It is an advantage of the way we attack these problems that the formalism established and the results obtained remain valid for homogeneous beams as well. The numerical results for the critical forces can be applied to solve some stability problems in the engineering practice.

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Section: Introductionmentioning

confidence: 99%

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

2023

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Symmetric stiffness matrices for isoparametric finite elements in nonlinear elasticity

Valvo

2024

Comput Mech

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The article illustrates a position-based finite element formulation, which greatly simplifies the statement of nonlinear elasticity problems. The formulation adopts as main unknowns the nodal positions in the current configuration instead of the nodal displacements. As a result, simple analytical expressions are obtained of the secant and tangent stiffness matrices for general isoparametric finite elements. Contrary to most formulations of the literature, the secant stiffness matrices turn out to be symmetric. Furthermore, any hyperelastic constitutive law can be easily implemented. Specialised expressions are deduced for the stiffness matrices of a two-node truss bar element and a three-node planar triangular element. The validity of the proposed approach is illustrated through the analysis of a steep von Mises truss and Cook’s membrane. For illustration, the de Saint Venant–Kirchhoff and neo-Hookean material models are considered.

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Static and dynamic nonlinear behavior of a multistable structural system consisting of two coupled von Mises trusses

de Castro,

Orlando,

Gonçalves

2023

International Journal of Non-Linear Mechanics

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Theoretical and experimental analysis of the von Mises truss subjected to a horizontal load using a new hyperelastic model with hardening

Cited by 5 publications

References 44 publications

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

Symmetric stiffness matrices for isoparametric finite elements in nonlinear elasticity

Static and dynamic nonlinear behavior of a multistable structural system consisting of two coupled von Mises trusses

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