A volume-averaged nodal projection method for the Reissner-Mindlin plate model

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses

Consistent and stable meshfree Galerkin methods using the virtual element decomposition

Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth (nonpolynomial functions), and they do not rely on an underlying mesh structure for their construction. These features render meshfree methods to be particularly appealing for higher-order PDEs and for large deformation simulations of solid continua. However, a deficiency that still persists in meshfree Galerkin methods is the inaccuracies in numerical integration, which affects the consistency and stability of the method. Several previous contributions have tackled the issue of integration errors with an eye on consistency, but without explicitly ensuring stability. In this paper, we draw on the recently proposed virtual elementmethod, to present a formulation that guarantees both the consistency and stability of the approximate bilinear form.We adopt maximum-entropy meshfree basis functions, but other meshfree basis functions can also be used within this framework. Numerical results for several two-dimensional and three-dimensional elliptic (Poisson and linear elastostatic) boundary-value problems that demonstrate the effectiveness of the proposed formulation are presented.National Science Foundation grant CMMI-1334783 to the University of California at Davis

A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition

In this article, we present a novel nodal integration scheme for meshfree Galerkin methods, which draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field variables, although the proposed scheme is applicable to any linear meshfree approximant. In our approach, the weak form integrals are nodally integrated using nodal representative cells that carry the nodal displacements and state variables such as strains and stresses. The nodal integration is performed using the virtual element decomposition, wherein the bilinear form is decomposed into a consistency part and a stability part that ensure consistency and stability of the method. The performance of the proposed nodal integration scheme is assessed through benchmark problems in linear and nonlinear analyses of solids for small displacements and small-strain kinematics. Numerical results are presented for linear elastostatics and linear elastodynamics and viscoelasticity. We demonstrate that the proposed nodally integrated meshfree method is accurate, converges optimally, and is more reliable and robust than a standard cell-based Gauss integrated meshfree method

Node-based uniform strain virtual elements for compressible and nearly incompressible plane elasticity

We propose a combined nodal integration and virtual element method for compressible and nearly incompressible plane elasticity, wherein the strain is averaged at the nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements. We refer to these new elements as node-based uniform strain virtual elements (NVEM). No additional degrees of freedom are introduced in this approach, thus resulting in a displacement-based formulation. A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations. Through several benchmark problems in plane elasticity, we demonstrate that the NVEM is accurate and optimally convergent, and devoid of volumetric locking in the nearly incompressible limit

LANSCE DRIFT TUBE LINAC WATER CONTROL SYSTEM REFURBISHMENT* -cc Creative Commons Attribution 3.0 (CC BY 3.0)

Abstract There are several refurbishment projects underway at the Los Alamos National Laboratory LANSCE linear accelerator. Systems involved are: RF, water cooling, networks, diagnostics, timing, controls, etc. The Drift Tube Linac (DTL) portion of the accelerator consists of four DTL tanks, each with three independent water control systems. The systems are about 40 years old, use outdated and non-replaceable equipment and NIM bin control modules, are beyond their design life and provide unstable temperature control. Insufficient instrumentation and documentation further complicate efforts at maintaining system performance. Detailed design of the replacement cooling systems is currently in progress. Previous design experience on the SNS accelerator water cooling systems will be leveraged, see the SNS DTL FDR OVERVIEW LANSCE Drift Tube Linac Water Cooling Systems The LANSCE Drift Tube Linac consists of 4 tanks. Each tank is supported by three water cooling systems: drift tube, tank wall, and quad magnet. Currently each water cooling system includes: a mix tank water supply and return manifolds water sub-manifolds manually operated isolation valves an automated valve to control the amount of chilled water flowing into the mix tank an automated water pump to maintain flow/pressure in the cooling loop an automated heater to add heat to the water when the Radio Frequency (RF) System is off temperature sensors read by the control system as control inputs for the valve, pump and heater pressure, temperature and water flow sensors read by the control system for sub-manifold monitoring water flow switches, read by the control system, for monitoring low water flows to individual Linac components Refurbishment Plan An engineering team has been assembled to design all mechanical, electrical, instrumentation and control aspects of the water systems. The planned approach is, in this fiscal year FY 2011, to complete the water cooling system design for the DTL tank which would improve accelerator operations most significantly. Then duplicate and fit the design to the other three tanks in fiscal year 2012. Procurement and assembly for the first tank are also planned for FY 2012. Installation, testing, commissioning and release for production are planned for early calendar year 2013. Although considerable and notable progress has been made on the mechanical engineering aspects of this project the focus of this paper is on the instrumentation and controls system portion, or more specifically the control system automation hardware and software design. A water system test stand is under construction which will be used to validate instrumentation selection; automation control system hardware and software platforms, controls methodology, closed and open loop logic schemes, as well as interlock and alarm monitoring, responses and actions. Engineering solutions to hardware layouts, processor load balancing, interfaces and integration into the LANSCE Control System (LCS) will also be tested and proven. CONTROL SYSTEM DESIGN OVERVIEW The new control system will consist of one programmable controller per tank to include control and monitoring of the three water cooling loops, effectively combining and enhancing the capabilities of the old control systems One new control system will simultaneously monitor and control three separate water cooling circuits on a single tank. The National Instruments (NI) Compact RIO (cRIO) is the selected programmable automation controller. The cRIO include

Basic principles of virtual element methods

ABSTRACT Over the past two decades, meshfree methods (MMs) as a numerical tool for solving PDEs have been welldeveloped. In contrast to finite elements, MMs do not require a mesh to construct the basis functions, which are smooth and non-polynomial functions. This feature makes MMs more appealing for the discretization of field variables in problems where, for instance, higher-order smoothness is needed or mesh distortions introduce a limitation for standard finite elements. Nonetheless, Galerkin MMs require background cells to perform the numerical integration of the weak form integrals. Usually, Gauss integration is employed on a background mesh of finite elements. This introduces integration errors that affect the accuracy, convergence and stability of the method. Several authors have tried to overcome the integration issue resulting in integration schemes that only ensure consistency and substantially improve accuracy, but stability is not guaranteed. In this work, a new approach for Galerkin MMs is introduced, which draws on the recently proposed Virtual Element Method [1], to ensure both consistency and stability of the approximate bilinear form. Benchmark examples in two-and three-dimensions will be presented to demonstrate the accuracy, consistency and stability of the method for Poisson and linear elasticity boundary-value problems. REFERENCES [1] L