Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

(Appendix 1) Coral analysis and isostatic rebound effects from different Holes of IODP Expedition 310

Past sea-level records provide invaluable information about the response of ice sheets to climate forcing. Some such records suggest that the last deglaciation was punctuated by a dramatic period of sea-level rise, of about 20 metres, in less than 500 years. Controversy about the amplitude and timing of this meltwater pulse (MWP-1A) has, however, led to uncertainty about the source of the melt water and its temporal and causal relationships with the abrupt climate changes of the deglaciation. Here we show that MWP-1A started no earlier than 14,650 years ago and ended before 14,310 years ago, making it coeval with the Bølling warming. Our results, based on corals drilled offshore from Tahiti during Integrated Ocean Drilling Project Expedition 310, reveal that the increase in sea level at Tahiti was between 12 and 22 metres, with a most probable value between 14 and 18 metres, establishing a significant meltwater contribution from the Southern Hemisphere. This implies that the rate of eustatic sea-level rise exceeded 40 millimetres per year during MWP-1A.

Advice to a mother on the management of her children : and on the treatment on the moment of some of [sic] their more pressing illnesses and accidents /

Includes index.

Hot-pressing of electrolytic, dehydrided, and calcium-reduced thorium powders /

"Contract AT-30-1 GEN-366."

Problems on the theory of the process of pressing metal powders and their mixtures.

"Translation of: Nekotoryye voprosy teorii protsessa pressovaniva metallicheskih poroshkov i ikh smesey." (romanized form)

The great alternative, an examination of six pressing concerns in today's world;

Mode of access: Internet.

Protecting investment values in land : conserving soil resources-a pressing national problem /

Mode of access: Internet.

The riddle of the Rhine; chemical strategy in peace and war. An account of the critical struggle for power and for the decisive war initiative. The campaign fostered by the great Rhine factories, and the pressing problems which they represent. A matter of pre-eminent public interest concerning the sincerity of disarmament, the future of warfare, and the stability of peace.

"The existence of this giant monopoly [Interessen gemeinschaft der deutschen teerfarbenfabriken] raises vital military and economic questions, which are ... 'The riddle of the Rhine'."--p. 14.

Some pressing educational needs of Virginia; measures advocated by the Committee of Twenty-five appointed by the Virginia Educational Conference ...

Mode of access: Internet.

Problems of American civilization, their practical solution the pressing Christian duty of today

First published in National perils and opportunities, discussions of the general Christian conference held in Washington, D.C., 1887 under the auspices of the Evangelical alliance for the United States. New York,1887.

Laws, rules and regulations relating to cleaning, dyeing, pressing, furrier and hat renovating establishments,

At head of title: State of California. Dept. of Professional and Vocational Standards. State Board of Dry Cleaners.

Microstructural and magnetic properties of Nd-Fe-B alloys processed by equal-channel angular pressing

Equal-channel angular pressing (ECAP) is a well-established thermo-mechanical processing technique. This technique allows virtually unlimited strain and manipulation of texture by processing route, while the cross-section of the sample remains unchanged during processing. In order to clarify the effectiveness of ECAP on preparing anisotropic permanent magnets, the microstructure and magnetic properties of a melt-spun Nd13.5Fe73.8Co6.7B5.6Ga0.4 alloy processed at 773-K for 300-s by ECAP were investigated. Macrotexture analysis carried out for the exit channel of ECAP shows that the basal plane of the tetragonal Nd2Fe14B crystal aligns parallel to the shear band, i.e., the c-axis texture formation normal to the shear band induced by the ECAP process. Due to this texture formation, the technical magnetization behaviour becomes anisotropic, and the remanent magnetization is clearly enhanced along the direction perpendicular to the shear band. This anisotropic microstructure is realized at a relatively low processing temperature of 773-K, well below the melting point of the Nd-rich intergranular phase. As a consequence of this lower processing temperature, the nanostructure of the melt-spun alloy remains approximately 20 to 30-nm, considerably smaller than the typical grain size obtained after conventional die-upsetting. Our study demonstrates that equal-channel angular pressing has a potential for realising anisotropic nanostructured magnets.

Enhanced superplasticity of magnesium alloy AZ31 obtained through equal-channel angular pressing with back-pressure

Excellent superplastic elongations (in excess of 1,200%) were achieved in a commercial cast AZ31 alloy processed by low temperature equal-channel angular pressing (ECAP) with a back-pressure to produce a bimodal grain structure. In contrast, AZ31 alloy processed by ECAP at temperatures higher than 200 °C showed a reasonably uniform grain structure and relatively low ductility. It is suggested that a bimodal grain structure is advantageous because the larger grains contribute to strain hardening thus delaying the onset of necking, while grain boundary sliding associated with small grains provides a stabilizing effect due to enhanced strain rate sensitivity. © 2008 Springer Science+Business Media, LLC.

Enhanced superplasticity in a magnesium alloy processed by equal-channel angular pressing with a back-pressure

An investigation was initiated to evaluate the feasibility of using equal-channel angular pressing (ECAP) to obtain high superplastic elongations in the AZ31 alloy with a back pressure producing a bimodal grain structure. Processing by ECAP was performed using a die with an angle of 90 ° between the two parts of the channel and a ram velocity of 15-20 mm/sec. Some pressing were conducted with a back-pressure by making use of a backward punch in the exit channel of the die. Molybdenum disulphide and a graphite spray were used as lubricants and billets were pressed using processing route B c in which each billet is rotated by 90 °. The pressing were conducted at temperatures in the range from 423 to 523 K and every billet was quenched in water after each pass. The significance of the bimodal microstructure is attributed to the ability of the larger grains to more easily accommodate grain boundary sliding through intragranular slip and twinning and to contribute to the strain hardening capability.