Form-finding and analysis of an alternative tensegrity dome configuration

2017 ◽  
Vol 20 (11) ◽  
pp. 1644-1657 ◽  
Author(s):  
Fatih Uzun
Keyword(s):  
Potential Energy ◽  
Energy Minimization ◽  
Minimum Potential Energy ◽  
Form Finding ◽  
Tensegrity Structures ◽  
Minimum Potential ◽  
Local Impact ◽  
Cable Dome ◽  
Minimization Approach ◽  
Cable Domes

Geiger domes are composed of cable and strut elements. This property of cable domes is the same as tensegrity structures, but in contraction to tensegrity structures, strut elements do not have a function that balances tension in cable elements with compression. In this study, a new cable dome configuration, that mimics the form of tensegrities, is proposed which is able to spread effect of an applied load into all elements of the dome and reduces its local impact. Form-finding and analysis of the Geiger and new dome configurations are performed based on the principle of minimum potential energy. Self-equilibrium forms with minimum potential energy are determined using genetic algorithms. The ability of genetic algorithm based potential energy minimization approach to perform form-finding of loaded or load free cable domes is investigated. Performance of the proposed configuration is tested and compared with the Geiger configuration under various loading conditions.

2. Does form follow function?

2014 ◽  
Author(s):  
David Blockley
Keyword(s):  
Potential Energy ◽  
Degrees Of Freedom ◽  
Minimum Potential Energy ◽  
Form Finding ◽  
Internal Forces ◽  
Minimum Potential ◽  
The Way

In c.15 bc, the Roman Vitruvius stated that a good building should satisfy three requirements: durability, utility, and beauty. ‘Does form follow function?’ examines utility and beauty. It explains that structures are naturally lazy because they contain minimum potential energy. Each piece of structure, however small or large, will move, but not freely as the neighbouring pieces will get in the way. When this happens internal forces are created as the pieces bump up against each other. Force pathways are degrees of freedom and the structure has to be strong enough to resist these internal forces along these pathways. Form-finding structures are exciting and innovative examples of the fusion of engineering and architecture.

Principles of minimum potential energy and complementary energy

2020 ◽  
pp. 228-248
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Boundary Condition ◽  
Potential Energy ◽  
Displacement Field ◽  
Mixed Boundary ◽  
Energy Functional ◽  
The Body ◽  
Minimum Potential Energy ◽  
Complementary Energy ◽  
Minimum Potential ◽  
Potential Energy Functional

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.

Optimization for Minimum Potential Energy, Maximum Rigidity and Minimum Deformability

1984 ◽  
pp. 9-87
Author(s):  
Andrej M. Brandt ◽  
Wojciech Dzieniszewski ◽  
Stefan Jendo ◽  
Wojciech Marks ◽  
Stefan Owczarek ◽  
...  
Keyword(s):  
Potential Energy ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
Energy Maximum

A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)

1994 ◽  
Vol 61 (4) ◽  
pp. 914-918 ◽  
Author(s):  
J. E. Taylor
Keyword(s):  
Potential Energy ◽  
Problem Formulation ◽  
Extremum Problem ◽  
Equilibrium Analysis ◽  
Minimum Potential Energy ◽  
Problem Statement ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

Buckling Analysis of a Bi-Directional Strain-Gradient Euler–Bernoulli Nano-Beams

2020 ◽  
Vol 20 (11) ◽  
pp. 2050114
Author(s):  
Murat Çelik ◽  
Reha Artan
Keyword(s):  
Potential Energy ◽  
Gradient Elasticity ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Minimum Potential Energy ◽  
End Conditions ◽  
Graded Material ◽  
Minimum Potential ◽  
Gradient Elasticity Theory ◽  
Basic Equations

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed.

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