Point configurations that are asymmetric yet balanced

A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in R^3, and his classification is equivalent to the converse for R^3. In this paper we disprove the converse in high dimensions. We construct several counterexamples, including one with trivial symmetry group.Comment: 10 page

Optimum structure for a uniform load over multiple spans

This paper presents a new half-plane Michell structure that transmits a uniformly distributed load of infinite horizontal extent to a series of equally-spaced pinned supports. Full kinematic description of the structure is obtained for the case when the maximum allowable tensile stress is greater than or equal to the allowable compressive stress. Although formal proof of optimality of the solution presented is not yet available, the proposed analytical solution is supported by substantial numerical evidence, involving the solution of problems with in excess of 10 billion potential members. Furthermore, numerical solutions for various combinations of unequal allowable stresses suggest the existence of a family of related, simple, and practically relevant structures, which range in form from a Hemp-type arch with vertical hangers to a structure which strongly resembles a cable-stayed bridge

Optimal Plastic Design for Partially Preassigned Strength Distribution

BRIEF NOTES 2iP 2,P 2iP | T T i £ tistically admissible stress field M(X) can only be optimal if at moment values M i (i = 1, 2, . . ., n) the rotations given by equations (l)-(3) result in a kinematically admissible displacement field (necessary condition). Example. For a clamped beam with three point loads, Since the slope of the moment diagram in the outer half of the beam is three times that in the inner half, equation The foregoing theorem admits an infinite number of solutions corresponding to 2.625 aP < x -3.25 aP. The moment diagrams for the limiting cases are shown in Remark. The proposed theorem is not related directly to Foulkes' theorem [2] and its extensions [6] because the latter preassign a specified strength distribution to given subsets of the structure. In the problem considered, the cost function is discontinuous but the subsets of the structure over which various regimes of the cost function apply are not preassigned. Hence the proposed extension of the Prager-Shield theory gives a more economical design than Foulkes' method

A review of new fundamental principles in exact topology optimization

Abstract After reviewing briefly the history of exact topology optimization of structures, a number of fundamental principles for deriving new optimal structural layouts will be presented. These also throw some light on general properties of optimal topologies

On the prediction of topology and local properties for optimal trussed structures

A new formulation is presented for mathematical modelling to predict the distribution of material, material properties, and topology for the optimal design of trussed structures. The design problem is cast in a form to minimize a measure of generalized compliance , which is calculated as a sum over the structure of weighted displacement. Member stiffnesses appear as design variables and, starting with a given ground structure, the solution predicts the optimal layout and distribution of stiffness. The isoperimetric constraint in the reformulated problem measures total cost in generalized form , based on independently specified unit relative cost factors for each truss element. One or another form of optimal design is generated via a process where designated elements in the unit relative cost field are adjusted systematically at each cycle. The generalized cost feature provides as well for the introduction of certain technical constraints into the design problem, e.g. the facility to design around obstacles. Results for each cycle of an algorithm for computational treatment are identified as the solution to a properly posed optimization problem. Computational procedures are demonstrated by the prediction of optimal designs for a variety of truss problems in 2D.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46074/1/158_2005_Article_BF01197558.pd

liteITD a MATLAB Graphical User Interface (GUI) program for topology design of continuum structures

Over the past few decades, topology optimization has emerged as a powerful and useful tool for the design of structures, also exploiting the ever growing computational speed and power. The design process has also been affected by computers which changed the concept of form into the concept of formation and the emergence of digital design. Topology optimization can modify existing designs, incorporate explicit features into a design and generate completely new designs. This paper will show how topology optimization can be used as a digital tool. The liteITD (lite version of Isolines Topology Design) software package will be described with the purpose of providing a tool for topology design. The liteITD program solves the topology optimization of two-dimensional continuum structures using von Mises stress isolines under single or multiple loading conditions, with different material properties in tension and compression, and multiple materials. The liteITD program is fully implemented in the MATrix LABoratory (MATLAB) software environment of MathWorks under Windows operating system. GUIDE (Graphical User Interface Development Environment) was used to create a friendly Graphical User Interface (GUI). The usage of this application is directed to students mainly (educational purposes), although also to designers and engineers with experience. The liteITD program can be downloaded and used for free from the website: http://www.upct.es/goe/software/liteITD.php

Topology synthesis of multi-input-multi-output compliant mechanisms.

A generalized formulation to design Multi-Input-Multi-Output (MIMO) compliant mechanisms is presented in this work. This formulation also covers the simplified cases of the design of Multi-Input and Multi-Output compliant mechanisms, more commonly used in the literature. A Sequential Element Rejection and Admission (SERA) method is used to obtain the optimum design that converts one or more input works into one or more output displacements in predefined directions. The SERA procedure allows material to flow between two different material models: 'real' and 'virtual'. The method works with two separate criteria for the rejection and admission of elements to efficiently achieve the optimum design. Examples of Multi-Input, Multi-Output and MIMO compliant mechanisms are presented to demonstrate the validity of the proposed procedure to design complex complaint mechanisms

Topology synthesis of multi-material compliant mechanisms with a Sequential Element Rejection and Admission method

The design of multi-material compliant mechanisms by means of a multi Sequential Element Rejection and Admission (SERA) method is presented in this work. The SERA procedure was successfully applied to the design of single-material compliant mechanisms. The main feature is that the method allows material to flow between different material models. Separate criteria for the rejection and admission of elements allow material to redistribute between the predefined material models and efficiently achieve the optimum design. These features differentiate it to other bi-directional discrete methods, making the SERA method very suitable for the design of multi-material compliant mechanisms. Numerous examples are presented to show the validity of the multi SERA procedure to design multi-material compliant mechanisms