Abstract: An N×N matrix is generated from computerized model representing a physical domain, comprises coefficients of N simultaneous linear equations with N unknown physical quantities associated with N degrees-of-freedom of the physical domain, and is represented by an undirected graph having N vertices connected by a plurality of edges. A best suitable partition scheme for dividing the N vertices into a separator group and, first and second mutually independent groups as follows: distance vectors of source vertices selected from the N vertices are calculated; for each distinct pair of the source vertices, the difference of respective distance vectors is used for finding a coarse graph whose adjacency coarse matrix is pentadiagonal; a trial partition scheme is determined using the coarse graph initially; the separator group is then iteratively improved by trimming vertices contained therein and merging them into one of the mutually independent groups until the separator group becomes minimal.

Abstract: An N×N matrix is generated from computerized model representing a physical domain, comprises coefficients of N simultaneous linear equations with N unknown physical quantities associated with N degrees-of-freedom of the physical domain, and is represented by an undirected graph having N vertices connected by a plurality of edges. A best suitable partition scheme for dividing the N vertices into a separator group and, first and second mutually independent groups as follows: distance vectors of source vertices selected from the N vertices are calculated; for each distinct pair of the source vertices, the difference of respective distance vectors is used for finding a coarse graph whose adjacency coarse matrix is pentadiagonal; a trial partition scheme is determined using the coarse graph initially; the separator group is then iteratively improved by trimming vertices contained therein and merging them into one of the mutually independent groups until the separator group becomes minimal.

Abstract: Systems and methods of limiting contact penetration in numerical simulation of non-linear structure response using implicit finite element analysis are described. According to one aspect, a finite element analysis (FEA) model of a structure is defined as a number of nodes and elements based on geometry and material properties of the structure. A time-marching analysis of the FEA model is then performed. The time-marching analysis results contain a number of solutions of non-linear structure response at respective time steps. Solution at each time step requires at least one iteration to compute. Non-linear structure response is determined in the following manner: 1) determining a search direction; 2) calculating a contact penetration parameter in the search direction; and 3) finding a minimum energy imbalance location along the search direction as a solution which is further restricted by the CPP such that contact penetration of the structure is substantially limited.

Abstract: A method of treating a blank of an aluminium base alloy comprising a combination of heat treatments and cold forming operations to produce a highly recovered semi-fabricated wrought product that is not statically recrystallized and that is inherently non-superplastic and is capable of superplastic deformation only after an initial non-superplastic deformation to achieve dynamic recrystallization.

Abstract: This invention relates to aluminium alloys containing lithium which are particularly suitable for aerospace construction in that they possess improved cold rolling characteristics optionally with improved damage tolerance. A method of producing sheet or strip material is described which comprises the steps of: (a) providing, in a condition suitable for hot rolling, a billet of an alloy of the composition in weight percent: lithium 1.9 to 2.6; magnesium 0.4 to 1.4; copper 1.0 to 2,2; manganese 9 to 0.09; zirconium 0 to 0.25; at least one other grain-controlling element 0 to 0.5; nickel 0 to 0.5; zinc 0 to 0.

Abstract: A method of and an apparatus for vertical, semi-continuous direct chill casting of light metal fabricating ingots of particularly, though not exclusively, lithium containing aluminium and magnesium alloys, through an open mould into a pit, comprising commencing the casting without a pool of water within the pit, supplying cooling water to the emergent ingot at a predetermined rate and continuously removing water from the pit as casting continues at a rate sufficient to ensure that no build up of a pool of water in the pit occurs, whereby the risk of violent and damaging explosion is further reduced.

Abstract: A method of superplastically deforming a blank of a metallic alloy which:1. has a composition suitable for superplastic deformation and2. has a grain structure suitable for superplastic deformation and3. contains less than that percentage of a constituent known to inhibit grain coarsening after recrystallization which is necessary for such inhibition,comprising raising the blank to a forming temperature, deforming the blank at a first strain rate to induce dynamic recrystallization and continuing to deform the blank at a second strain rate lower than the first rate.

Abstract: A method of superplastically forming an article from a light metal base alloy, of the kind capable of having its crystal structure modified by cold working in such a way that subsequent dynamic recrystallization by hot working is facilitated, comprises cold working a first blank of the alloy to form a second blank having the modified crystal structure, and then forming the second blank into the article by hot working so that dynamic recrystallization is induced and super plastic deformation occurs. The degree of modification of the crystal structure during cold working is such that as the dynamic recrystallization continues, the grain size is progressively refined.

Abstract: It has now been found that alloys of the type that are the cheapest and most widely used for the production of formed components may also be provided with superplastic properties. Such alloys may comprise a selected non-heat treatable base material together with dynamic recrystallization modifying additives to achieve fine structure. The base material may be aluminium of normal commercial purity and the additives 0.4% to 2% iron and 0.4 to 2% silicon; or the base material may be aluminium and 0.75 to 2.5% manganese and the additive 0.4 to 1% iron; or the base material may be aluminium and 0.25 to 0.75% manganese with no additive; or the base material may be aluminium and 1 to 4% magnesium and the additive 0.25 to 0.75% manganese. In all these cases at least one of the elements Zr, Nb, Ta and Ni must also be present in an amount of at least 0.3% substantially all of which is in solid solution and the total amount of said elements not exceeding 1%.

Abstract: Alloys having a composition suitable for superplastic deformation usually require heat treatment after casting and mechanical working in order to produce in the alloy the necessary fineness of grain stucture to permit such deformation to occur. It has now been found that some such alloys including in particular ranges of aluminum alloys containing zirconium (or Nb, Ta or Ni) may be heated to a superplastic forming temperature and non-superplastically deformed at that temperature to induce dynamic recrystallisation and simultaneously produce a fine recrystallised grain structure and superplastic deformation.