Analytical solutions for geometrically nonlinear trusses

Greco, Marcelo; Vicente, Carlos Eduardo Rodrigues

doi:10.1590/s0370-44672009000200012

Cited by 9 publications

(7 citation statements)

References 8 publications

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“…Figure 2 demonstrates the configuration of Von Mises Truss [35]. This simple example is mainly chosen to verify the proposed formulations and code implementations.…”

Section: The Von Mises Trussmentioning

confidence: 99%

Lagrangian interpolation for kinetic dynamic relaxation method with the variable load factor

Abbasi

Namadchi

Alamatian

2021

J Braz. Soc. Mech. Sci. Eng.

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Common dynamic relaxation (DR) methods use central finite differences to derive fundamental equations. In this study, Lagrangian interpolation functions are utilized to formulate iterative DR relationships with kinetic damping. This procedure leads to an algorithm that, unlike the ubiquitous DR methods, does not require the calculation of nodal velocities thereby marching forward only through successive nodal displacement. Also, the power iteration method is used to determine the optimal time-step ratio. By utilizing this time-step, the restarting analysis phase which is one of the drawbacks of the kinetic DR strategy is eliminated. Furthermore, a new variable load factor is developed based on the concept of minimization of displacement increment function. To evaluate the performance and efficiency of the proposed method, some truss and frame structures with geometrically nonlinear behavior are analyzed. Results prove that the number of convergence iterations and analysis time are reduced in the new kinetic DR scheme in comparison with other conventional DR methods.

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“…Figure 2 demonstrates the configuration of Von Mises Truss [35]. This simple example is mainly chosen to verify the proposed formulations and code implementations.…”

Section: The Von Mises Trussmentioning

confidence: 99%

Lagrangian interpolation for kinetic dynamic relaxation method with the variable load factor

Abbasi

Namadchi

Alamatian

2021

J Braz. Soc. Mech. Sci. Eng.

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“…The first study of a three-hinged rod system was conducted by R. V. Mises 6 and the systems themselves are called von Mises trusses. We conducted a wide range of studies, taking into account the elastic reactions of the system and elastic supports at the joints, 7,8 getting close to that of Zeman's machines. 9 There are researches of Stoker's column buckling.…”

Section: Introductionmentioning

confidence: 99%

Determining sloped-load limits inside von Mises truss with elastic support

Bilyk¹,

Tonkacheiev²

2018

Mater. Tehnol.

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The scientific novelty of this work lies in the description of the methods of calculating and analyzing the symmetrical stability loss of the von Mises truss in the case of sloped loads with an elastic support at the top of the truss. In this work, we consider a deformed layout of the von Mises truss with an elastic support under a concentrated load at the apex joint about the vertical axis. Numerical studies were carried out using the proposed methods. This work indicates the impact of the sloped load and elastic support on the truss' stability loss. We determined dependencies of critical external-load values on the rod's starting pitch for different situations. For each design situation, we obtained generalized expressions for determining critical force values for the truss' apex joint. We obtained dependencies and analytical expressions for determining the critical load on the dome structure, based on the initial geometrical parameters, taking into account the reaction of the elastic support at the apex joint and the direction of the external loads. Our studies show that increasing the support's stiffness increases the sustainability of the von Mises truss. Additionally, we obtained new results required for improving the stability of trusses under a sloped load with an angle of 10-40°about the vertical axis.

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“…Some of these works [5,[7][8] have shown how geometrical and material nonlinearities affects stability of truss systems and that if properly designed could lead to a desired state of equilibrium. Even with the success of these methods the need for an analytical method to improve universality when analyzing trusses with high geometrical nonlinearity [9] and to fully understand the behavior of these systems including general multistability criteria is recognized [10]. Space trusses analyzed in [8] by numerical methods have shown the possibility of developing a lattice structure that would exhibit multiple states of equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Cusp singularity-based bistability criterion for geometrically nonlinear structures

Danso

Karpov

2017

Extreme Mechanics Letters

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This letter introduces a method of analyzing multi-stable truss structures and unit cells of engineered materials using the third order derivative of the formulated system's potential energy function. The method can determine systematically all the cusp point singularities arising at the onset of bistability, and therefore identify the regions of hysteretic superelasticity and superplasticity from the usual geometrical nonlinearity in the solution space. The ability to design these behaviors is a great advantage that is highlighted with the example analysis of a bistable plane truss and a tetrahedral unit cell of a 3D lattice structure.

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Analytical solutions for geometrically nonlinear trusses

Abstract: Abstract

Cited by 9 publications

References 8 publications

Lagrangian interpolation for kinetic dynamic relaxation method with the variable load factor

Lagrangian interpolation for kinetic dynamic relaxation method with the variable load factor

Determining sloped-load limits inside von Mises truss with elastic support

Cusp singularity-based bistability criterion for geometrically nonlinear structures

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