Jaime Cervera Bravo

On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight

The details of the Theorem of Michell are examined. Some remarks are made about the quantity of structure and the Maxwell number of a framework and about the Michell optimality criterion. The two-loads bending problem is examined, comparing solutions derived from another one found by Sokół and Lewiński (Struct Multidisc Optim 42:835–853, 2010) with others obtained from simulated annealing (SA) search. The collected data suggest that the Michell theorem is a sufficient test for a framework to be optimal, but maybe no necessary. As a consequence, there could exist problems for which the theorem is useless.

On the layout of a least weight single span structure with uniform load

Beghini et al. (Struct Multidisc Optim 50:49–64, 2014) have published a very interesting paper arriving to practically the same nearly optimal solutions for the so named “bridge problem” that the writers published a year before, but using an alternative and remarkable approach to the problem. In spite of this general agreement, the writers think that some details of the paper can be improved and there are results that can be given a clear and meaningful interpretation, thanks to an old and practically unknown theorem on optimal slenderness.

Two Near-Optimal Layouts for Trusslike Bridge Structures Bearing Uniform Weight between Supports

Although the primary objective on designing a structure is to support the external loads, the achievement of an optimal layout that reduces all costs associated with the structure is an aspect of increasing interest. The problem of finding the optimal layout for bridgelike structures subjected to a uniform load is considered. The problem is formulated following a theory on economy of frame structures, using the stress volume as the objective function and including the selection of appropriate values for statically indeterminate reactions. It is solved in a function space of finite dimension instead of using a general variational approach, obtaining near-optimal solutions. The results obtained with this profitable strategy are very close to the best layouts known to date, with differences of less than 2% for the stress volume, but with a simpler layout that can be recognized in some real bridges. This strategy could be a guide to preliminary design of bridges subject to a wide class of costs.

Near-optimal solutions for two point loads between two supports

In a recent work, Sokół and Rozvany have shown a family of benchmark solutions for the two load problem, probably the optimal one. Taking into account that the difference in cost from previously known solutions was small, we have looked for a simpler albeit sub-optimal family of solutions. As a result, we have obtained three sub-optimal families, including one with a simple circular arc. The three families are compared with the benchmarks, and we have found that all three are of practical interest, because they increase the cost only by a small amount in spite of their simplicity.

On Galileo’s Tallest Column

The height at which an unloaded column will fail under its own weight was calculated for first time by Galileo for cylindrical columns. Galileo questioned himself if there exists a shape function for the cross section of the column with which it can attain a greater height than the cylindrical column. The problem is not solved since then, although the definition of the so named “constant maximum strength” solids seems to give an affirmative answer to Galileo’s question, in the form of shapes which seem to attain infinite height, even when loaded with a useful load at the top. The main contribution of this work is to show that Galileo’s problem is (i) an important problem for structural design theory of buildings and other structures, (ii) not solved by the time being in any sense, and (iii) an interesting problem for mathematicians involved in related but very different problems (as Euler’s tallest column). A contemporary formulation of the problem is included as a result of a research on the subject.