The GPRIME approach to finite element modeling

GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data

Mathematical determination of geometrical image aberrations in single and double mirror systems

Mathematical determination of geometrical image aberrations in single and double mirror system

How Prepared Are State and Local Workers for Retirement

A widespread perception is that state-local government workers receive high pension benefits which, combined with Social Security, provide more than adequate retirement income. The perception is consistent with multiplying the 2-percent benefit factor in most plan formulae by a 35- to 40- year career and adding a Social Security benefit. But this calculation assumes that individuals spend enough of their career in the public sector to produce such a retirement outcome. This brief summarizes the results of a paper that uses Health and Retirement Study (HRS) and actuarial reports published by state and local pension systems to test the hypothesis that state-local workers have more than enough money for retirement.

A Role for Defined Contribution Plans in the Public Sector

In the wake of the financial crisis, policymakers have been talking about shifting from defined benefit plans to defined contribution plans in the public sector. Three states – Georgia, Michigan, and Utah – have taken action, joining the 10 states that had introduced some form of defined contribution plans before 2008. Interestingly, these new plans are “hybrids” that combine elements of both defined benefit plans and defined contribution plans. Such an approach spreads the risks associated with the provision of retirement income between the employer and the employee. This brief provides an update on defined contribution initiatives in the public sector and then discusses whether the hybrids that have been introduced are the best way to combine the two plan types. The brief proceeds as follows. The first section discusses the issues involved with moving from a defined benefit plan to a defined contribution arrangement. The second section recaps the role that defined contribution plans played in the public sector before the financial crisis. The third section describes the new hybrid plans recently adopted in Georgia, Michigan, and Utah. And the fourth section suggests that a better type of hybrid might be one where defined contribution plans are “stacked” on the state’s defined benefit plan rather than placed alongside of it. The fifth section concludes that defined contribution plans have a role in the public sector, but that role is supplementing, not replacing, defined benefit plans.

Can State and Local Pensions Muddle Through?

The finances of state and local pension plans are headline news almost daily.1 Indeed, although these plans were moving toward prefunding their promised benefits, two financial crises in 10 years have thrown them seriously off course. Measured by the standards of the Government Accounting Standards Board, between 2008 and 2009 the ratio of assets to liabilities for our sample of 126 plans dropped from 84 percent to 79 percent. But this decline is only the beginning of the bad news that will emerge as the losses are spread over the next several years. Furthermore, the funded levels are closer to 50 percent if liabilities are discounted by a riskless rate, as recommended by economists and financial experts.2 What do these numbers imply for the future of these plans? Here’s what’s happening. States and localities have increased contributions and extended retirement ages for new employees, but these changes will take a long time to have any substantial effect. In most states, constitutional protections and court rulings have prohibited public employers from cutting benefits for existing employees. Thus, the only option for a quick fix would be an infusion of tax revenues. But the recession has decimated tax revenues and increased the demand for state and local services. Thus, the question is whether these plans have enough assets to muddle along until the economy and the stock market recover. Or do they face a liquidity crisis? That is the subject of this brief. The discussion is as follows. The first section looks at the simple ratio of assets to benefits over time and across plans in 2009. The second section moves to a more dynamic approach and investigates two concepts for estimating when plans would run out of money. Under a “termination” concept, where benefits earned to date and plan assets are put in an “old” plan and normal cost payments cover all future accruals, most plans have enough assets to last for at least 15 years. Under a more realistic “ongoing” framework, where normal costs are used to cover benefit payments, most plans have enough for at least 30 years.

Silsesquioxanes as precursors to ceramic composites

Silsesquioxanes having the general structure RSiO sub 1.5, where R = methyl, propyl, or phenyl, melt flow at 70 to 100 C. Above 100 C, free -OH groups condense. At 225 C further crosslinking occurs, and the materials form thermosets. Pyrolysis, with accompanying loss of volatiles, takes place at nominally 525 C. At higher temperatures, the R group serves as an internal carbon soruce for carbo-thermal reduction to SiC accompanied by the evolution of CO. By blending silsesquioxanes with varying R groups, both the melt rheology and composition of the fired ceramic can be controlled. Fibers can be spun from the melt which are stable in argon in 1400 C. The silsesquioxanes also were used as matrix precursors for Nicalon and alpha-SiC platelet reinforced composites