scholarly journals On the continuum properties of repetitive beam-like pin-jointed structures

2002 ◽  
Vol 37 (5) ◽  
pp. 459-464
Author(s):  
N G Stephen ◽  
Y Zhang
Keyword(s):  
Potential Energy ◽  
Single Cell ◽  
Stiffness Matrix ◽  
Minimum Potential Energy ◽  
One Dimensional ◽  
Displacement Vectors ◽  
Repetitive Structure ◽  
Minimum Potential ◽  
Equivalent Continuum ◽  
The Continuum

The equivalent continuum beam properties of a one-dimensional repetitive structure have previously been determined through eigenanalysis of the transfer matrix of a single cell. A simpler procedure requires a knowledge of the stiffness matrix of the single cell, together with the ability to deduce the displacement vectors for tension, bending and shear. A once and for all application of the principle of minimum potential energy for tension yields the equivalent continuum Poisson's ratio, from which the remaining properties follow.

Optimization of Finite Element Grids Based on Minimum Potential Energy

1973 ◽  
Vol 95 (1) ◽  
pp. 186-190 ◽  
Author(s):  
G. M. McNeice ◽  
P. V. Marcal
Keyword(s):  
Finite Element ◽  
Potential Energy ◽  
Axial Load ◽  
Necessary Conditions ◽  
Nodal Point ◽  
Initial Study ◽  
Minimum Potential Energy ◽  
One Dimensional ◽  
Independent Variables ◽  
Minimum Potential

An initial study has been made of a method for optimizing finite element grids. This method is based on the minimum potential energy where the nodal point positions are also treated as independent variables. Necessary conditions have been obtained for the optimized grids. Case studies demonstrate the procedure for a one-dimensional tapered bar under axial load and for a two-dimensional square membrane subjected to a parabolic tensile stress. The optimized grids were observed to give improved stress estimates.

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
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