Table of Contents

I. Verification Test Case Descriptions
1. Introduction
1.1. Program Overview
1.2. Program Verification
1.3. Finding Test Cases of Interest
1.4. Accessing Test Case Inputs
1.5. Verification Manual Versus Other Manuals
1.6. Verification Manual Contents
1.7. Expected Results
1.8. Test Case Selection and Method of Solution
1.9. Numerical Comparisons
1.10. References
1.11. Test Case Format
1.12. Symbols and Nomenclature
1.13. Memory Requirements and Run Times
1.14. Abbreviation and Symbol List
1.15. Units Abbreviation List
1.16. Index by Element Number
VM1 - Statically Indeterminate Reaction Force Analysis
VM2 - Beam Stresses and Deflections
VM3 - Thermally Loaded Support Structure
VM4 - Deflection of a Hinged Support
VM5 - Laterally Loaded Tapered Support Structure
VM6 - Pinched Cylinder
VM7 - Plastic Compression of a Pipe Assembly
VM8 - Parametric Calculation of Point-to-Point Distances
VM9 - Large Lateral Deflection of Unequal Stiffness Springs
VM10 - Bending of a Tee-Shaped Beam
VM11 - Residual Stress Problem
VM12 - Combined Bending and Torsion
VM13 - Cylindrical Shell Under Pressure
VM14 - Large Deflection Eccentric Compression of a Column
VM15 - Bending of a Circular Plate Using Axisymmetric Elements
VM16 - Bending of a Solid Beam (Plane Elements)
VM17 - Snap-Through Buckling of a Hinged Shell
VM18 - Out-of-Plane Bending of a Curved Bar
VM19 - Random Vibration Analysis of a Deep Simply-Supported Beam
VM20 - Cylindrical Membrane Under Pressure
VM21 - Tie Rod with Lateral Loading
VM22 - Small Deflection of a Belleville Spring
VM23 - Thermal-structural Contact of Two Bodies
VM24 - Plastic Hinge in a Rectangular Beam
VM25 - Stresses in a Long Cylinder
VM26 - Large Deflection of a Cantilever
VM27 - Thermal Expansion to Close a Gap
VM28 - Transient Heat Transfer in an Infinite Slab
VM29 - Friction on a Support Block
VM30 - Solid Model of Surface Fillet
VM31 - Cable Supporting Hanging Loads
VM32 - Thermal Stresses in a Long Cylinder
VM33 - Transient Thermal Stress in a Cylinder
VM34 - Bending of a Tapered Plate (Beam)
VM35 - Bimetallic Layered Cantilever Plate with Thermal Loading
VM36 - Limit Moment Analysis
VM37 - Elongation of a Solid Bar
VM38 - Internal Pressure Loading of a Thick-Walled Cylinder
VM39 - Bending of a Circular Plate with a Center Hole
VM40 - Large Deflection and Rotation of a Beam Pinned at One End
VM41 - Small Deflection of a Rigid Beam
VM42 - Barrel Vault Roof Under Self Weight
VM43 - Bending of an Axisymmetric Thick Pipe
VM44 - Bending of an Axisymmetric Thin Pipe
VM45 - Natural Frequency of a Spring-Mass System
VM46 - 2-D End Notched Flexure Problem
VM47 - Torsional Frequency of a Suspended Disk
VM48 - Natural Frequency of a Motor-Generator
VM49 - Electrostatic Field Analysis of Quadpole Wires
VM50 - Fundamental Frequency of a Simply Supported Beam
VM51 - Electrostatic Forces Between Charged Spheres
VM52 - Automobile Suspension System Vibration
VM53 - Vibration of a String Under Tension
VM54 - Vibration of a Rotating Cantilever Blade
VM55 - Vibration of a Stretched Circular Membrane
VM56 - Hyperelastic Thick Cylinder Under Internal Pressure
VM57 - Torsional Frequencies of a Drill Pipe
VM58 - Centerline Temperature of a Heat Generating Wire
VM59 - Lateral Vibration of an Axially-loaded Bar
VM60 - Natural Frequency of a Cross-ply Laminated Shell
VM61 - Longitudinal Vibration of a Free-free Rod
VM62 - Vibration of a Wedge
VM63 - Static Hertz Contact Problem
VM64 - Thermal Expansion to Close a Gap at a Rigid Surface
VM65 - Transient Response of a Ball Impacting a Flexible Surface
VM66 - Vibration of a Flat Plate
VM67 - Radial Vibrations of a Circular Ring
VM68 - PSD Response of a Two DOF Spring-mass System
VM69 - Seismic Response
VM70 - Seismic Response of a Beam Structure
VM71 - Transient Response of a Spring-Mass-Damper System
VM72 - Logarithmic Decrement
VM73 - Free Vibration with Coulomb Damping
VM74 - Transient Response to an Impulsive Excitation
VM75 - Transient Response to a Step Excitation
VM76 - Harmonic Response of a Guitar String
VM77 - Transient Response to a Constant Force
VM78 - Transverse Shear Stresses in a Cantilever Beam
VM79 - Transient Response of a Bilinear Spring Assembly
VM80 - Plastic Response to a Suddenly Applied Constant Force
VM81 - Transient Response of a Drop Container
VM82 - Simply Supported Laminated Plate Under Pressure
VM83 - Impact of a Block on a Spring Scale
VM84 - Displacement Propagation along a Bar with Free Ends
VM85 - Transient Displacements in a Suddenly Stopped Moving Bar
VM86 - Harmonic Response of a Dynamic System
VM87 - Equivalent Structural Damping
VM88 - Response of an Eccentric Weight Exciter
VM89 - Natural Frequencies of a Two-mass-spring System
VM90 - Harmonic Response of a Two-Mass-Spring System
VM91 - Large Rotation of a Swinging Pendulum
VM92 - Insulated Wall Temperature
VM93 - Temperature Dependent Conductivity
VM94 - Heat-generating Plate
VM95 - Heat Transfer from a Cooling Spine
VM96 - Temperature Distribution in a Short, Solid Cylinder
VM97 - Temperature Distribution Along a Straight Fin
VM98 - Temperature Distribution Along a Tapered Fin
VM99 - Temperature Distribution in a Trapezoidal Fin
VM100 - Heat Conduction Across a Chimney Section
VM101 - Temperature Distribution in a Short Solid Cylinder
VM102 - Cylinder with Temperature Dependent Conductivity
VM103 - Thin Plate with Central Heat Source
VM104 - Liquid-Solid Phase Change
VM105 - Heat Generating Coil with Temperature Conductivity
VM106 - Radiant Energy Emission
VM107 - Thermocouple Radiation
VM108 - Temperature Gradient Across a Solid Cylinder
VM109 - Temperature Response of a Suddenly Cooled Wire
VM110 - Transient Temperature Distribution in a Slab
VM111 - Cooling of a Spherical Body
VM112 - Cooling of a Spherical Body
VM113 - Transient Temperature Distribution in an Orthotropic Metal Bar
VM114 - Temperature Response to Increasing Temperature
VM115 - Thermal Response of a Heat-generating Slab
VM116 - Heat Conducting Plate with Sudden Cooling
VM117 - Electric Current Flowing in a Network
VM118 - Centerline Temperature of a Heat-generating Wire
VM119 - Centerline Temperature of an Electrical Wire
VM120 - Microstrip Transmission Line Capacitance
VM121 - Voltage Forced Coil
VM122 - Pressure Drop in a Turbulent Flowing Fluid
VM123 - Laminar Flow in a Piping System
VM124 - Discharge of Water from a Reservoir
VM125 - Radiation Heat Transfer Between Concentric Cylinders
VM126 - Heat Transferred to a Flowing Fluid
VM127 - Buckling of a Bar with Hinged Ends (Line Elements)
VM128 - Buckling of a Bar with Hinged Ends (Area Elements)
VM129 - Numerical Differentiation and Integration
VM130 - Fourier Series Generation for a Saw Tooth Wave
VM131 - Acceleration of a Rotating Crane Boom
VM132 - Stress Relaxation of a Tightened Bolt Due to Creep
VM133 - Motion of a Rod Due to Irradiation Induced Creep
VM134 - Plastic Bending of a Clamped I-Beam
VM135 - Bending of a Beam on an Elastic Foundation
VM136 - Large Deflection of a Buckled Bar (the Elastica)
VM137 - Large Deflection of a Circular Membrane
VM138 - Large Deflection Bending of a Circular Plate
VM139 - Bending of a Long Uniformly Loaded Rectangular Plate
VM140 - Stretching, Twisting and Bending of a Long Shaft
VM141 - Diametral Compression of a Disk
VM142 - Stress Concentration At a Hole in a Plate
VM143 - Fracture Mechanics Stress for a Crack in a Plate
VM144 - Bending of a Composite Beam
VM145 - Stretching of an Orthotropic Solid
VM146 - Bending of a Reinforced Concrete Beam
VM147 - Gray-Body Radiation within a Frustum of a Cone
VM148 - Bending of a Parabolic Beam
VM149 - Residual Vector in Mode-Superposition Harmonic Analysis
VM150 - Moisture Diffusion in a Plate Under Constant Surface Concentration
VM151 - Nonaxisymmetric Vibration of a Circular Plate
VM152 - 2-D Nonaxisymmetric Vibration of a Stretched Membrane
VM153 - 3-D Nonaxisymmetric Vibration of a Stretched Membrane
VM154 - Vibration of a Fluid Coupling
VM155 - Chaboche Rate-Dependent Plastic Material under Cyclic Loading
VM156 - Natural Frequency of a Nonlinear Spring-Mass System
VM157 - 3-D Acoustic Modal Analysis with Temperature Change
VM158 - Motion of a Bobbing Buoy
VM159 - Temperature-controlled Heater
VM160 - Solid Cylinder with Harmonic Temperature Load
VM161 - Heat Flow From an Insulated Pipe
VM162 - Cooling of a Circular Fin of Rectangular Profile
VM163 - Groundwater Seepage (Permeability Analogy)
VM164 - Drying of a Thick Wooden Slab (Diffusion Analogy)
VM165 - Current-Carrying Ferromagnetic Conductor
VM166 - Long Cylinder in a Sinusoidal Magnetic Field
VM167 - Transient Eddy Currents in a Semi-Infinite Solid
VM168 - Magnetic Field in a Nonferrous Solenoid
VM169 - Permanent Magnet Circuit With an Air Gap
VM170 - Magnetic Field From a Square Current Loop
VM171 - Permanent Magnet Circuit With an Elastic Keeper
VM172 - Stress Analysis of a Long, Thick, Isotropic Solenoid
VM173 - Centerline Temperature of an Electrical Wire
VM174 - Bimetallic Beam Under Thermal Load
VM175 - Natural Frequency of a Piezoelectric Transducer
VM176 - Frequency Response of Electrical Input Admittance
VM177 - Natural Frequency of a Submerged Ring
VM178 - 2-D Double Cantilever Beam Problem
VM179 - Dynamic Double Rotation of a Jointed Beam
VM180 - Bending of a Curved Beam
VM181 - Natural Frequency of a Flat Circular Plate
VM182 - Transient Response of a Spring-mass System
VM183 - Harmonic Response of a Spring-mass System
VM184 - Straight Cantilever Beam
VM185 - AC Analysis of a Slot Embedded Conductor
VM186 - Transient Analysis of a Slot Embedded Conductor
VM187 - Bending of a Curved Beam
VM188 - Force Calculation on a Current Carrying Conductor
VM189 - Stress Relaxation of a Chloroprene Rubber
VM190 - Ferromagnetic Inductor
VM191 - Hertz Contact Between Two Cylinders
VM192 - Cooling of a Billet by Radiation
VM193 - Evaluation of Stress Intensity Factor for an Inclined Crack Using XFEM Method
VM194 - Element Birth/Death in a Fixed Bar
VM195 - Toggle Mechanism
VM196 - Counter-Balanced Loads on a Block
VM197 - IGES Write/Read for Thick-Walled Cylinder
VM198 - Large Strain In-plane Torsion Test
VM199 - Viscoplastic Analysis of a Body (Shear Deformation)
VM200 - Viscoelastic Sandwich Seal Analysis
VM201 - Rubber Cylinder Pressed Between Two Plates
VM202 - Transverse Vibrations of a Shear Beam
VM203 - Dynamic Load Effect on Supported Thick Plate
VM204 - Solid Model of an Axial Bearing
VM205 - Earth Pressure Problem Using Mohr Coulomb Model
VM206 - Stranded Coil with Voltage Excitation
VM207 - Stranded Coil Excited by External Circuit
VM208 - RL Circuit with Controlled Source
VM209 - Static Analysis of Double Bellows Air Spring
VM210 - Pyramid Validation of Tetrahedron to Hexahedron
VM211 - Rubber Cylinder Pressed Between Two Plates
VM212 - DDAM Analysis of Foundation System (2-DOF System)
VM213 - Differential Inductance of a Transformer
VM214 - Rotating Rod in a Uniform Magnetic Field
VM215 - Thermal-Electric Hemispherical Shell with Hole
VM216 - Lateral Buckling of a Right Angle Frame
VM217 - Portal Frame Under Symmetric Loading
VM218 - Hyperelastic Circular Plate
VM219 - Frequency Response of a Prestressed Beam using APDL MATH Commands
VM220 - Electromigration Diffusion Problem with Perfectly Blocking Diffusion Barrier
VM221 - Simulation of Shape Memory Alloy Effect
VM222 - Warping Torsion Bar
VM223 - Electro-Thermal Microactuator Analysis
VM224 - Implicit Creep under Biaxial Load
VM225 - Rectangular Cross-Section Bar with Preload
VM226 - 1-D Advection Diffusion Problem
VM227 - Radiation Between Finite Coaxial Cylinders
VM228 - Radiation between Infinite Coaxial Cylinders
VM229 - Friction Heating of Sliding Block
VM230 - Radiation Between Two Concentric Spheres
VM231 - Piezoelectric Rectangular Strip Under Pure Bending Load
VM232 - Stress Intensity Factor for a Single Edge Crack with Pressure Load Using UMM Method
VM233 - Static Force Computation of a 3-D Solenoid Actuator
VM234 - Cyclic Loading of a Rubber Block
VM235 - Frequency Response of a Prestressed Beam
VM236 - Hysteresis Calculation of a Beam Under Electrostatic Load
VM237 - RLC Circuit with Piezoelectric Transducer
VM238 - Wheatstone Bridge Connection of Piezoresistors
VM239 - Mechanics of the Revolute and Universal Joints
VM240 - Thermal Expansion of Rigid Beams in a Composite Bar
VM241 - Static Force Computation of a 3-D Solenoid Actuator
VM242 - Johnson-Champoux-Allard Equivalent Fluid Model
VM243 - Cantilever Beam with Triangular Loading Defined by Function
VM244 - Modal Analysis of a Cyclic Symmetric Annular Plate
VM245 - Squeeze Film Damping: Rectangular Plate
VM246 - Cyclic Analysis of an End-Loaded Hollow Cylindrical Cantilever Beam
VM247 - Campbell Diagrams and Critical Speeds Using Symmetric Bearings
VM248 - Delamination Analysis of Double Cantilever Beam
VM249 - Gasket Material Under Uniaxial Compression Loading - 2-D Analysis
VM250 - Gasket Material Under Uniaxial Compression Loading - 3-D Analysis
VM251 - Shape Memory Alloy Under Uniaxial Tension Load
VM252 - Gurson Bar-Necking Benchmark with Applied Displacement - 2-D Analysis
VM253 - Gurson Hydrostatic Tension Benchmark - 3-D Analysis
VM254 - Campbell Diagrams and Critical Speeds Using Symmetric Orthotropic Bearings
VM255 - Delamination Analysis using Contact Based Debonding Capability
VM256 - Fracture Mechanics Stress for a Crack in a Plate using CINT Command
VM257 - Transient Analysis of a Swing with Two Rigid Links and Beam
VM258 - Spin-up Maneuver of a Flexible Beam
VM259 - Missing Mass with Rigid Responses Effects in Spectrum Analysis for BM3 Piping Model
VM260 - Two-Dimensional Consolidation Settlement Problem
VM261 - Rotating Beam with Internal Viscous Damping
VM262 - Two-Dimensional Fractural Problem under Thermal Loading
VM263 - Critical Speeds for a Rotor Bearing System with Axisymmetric Elements
VM264 - Terzaghi's One-Dimensional Consolidation Settlement Problem
VM265 - Elastic Rod Impacting a Rigid Wall
VM266 - 3-D Crossing Beams in Contact with Friction
VM267 - Inclined Crack in 2-D Plate Under Uniform Tension Loading
VM268 - Mullins Effect on a Rubber Tube Model Subjected to Tension Loading
VM269 - Deformation of Tube and Sphere Modeled with Neo-Hookean Material Model
VM270 - Forces in Permanent Magnets
VM271 - Convection Treatment Problem for a Hollow Cylinder with Fluid Flow
VM272 - 2-D and 3-D Frictional Hertz Contact
VM273 - Shape Memory Alloy With Thermal Effect Under Uniaxial Loading
VM274 - Stabilizing Squeal Damping
VM275 - Mode Lock-in and Friction Induced Vibrations of a Pin-Disc Model
VM276 - Moisture Diffusion in a Plate Under Constant Flux
VM277 - Hall Plate in a Uniform Magnetic Field
VM278 - Effect of a Pipe Lying on the Ground Under Gravity Loading
VM279 - T-Stress for a Crack in a Plate Using the CINT Command
VM280 - Conduction in a Doubly Insulated Pipe Carrying Steam
VM281 - Effect of Stress Stiffening and Spin Softening on a Rotating Plate
VM282 - Mode-Superposition Response Analysis of a Piston-Fluid System
VM283 - Low Reduced Frequency Model for Visco-thermal Fluid with Thin Structure
VM284 - Acceleration Solution in Response Spectrum Analysis Using Missing Mass Method
VM285 - Determining the C* Integral in a Single-Edge Cracked Plate Problem
VM286 - Wear of a Block Under Uniform Compression
VM287 - Initial Crack Growth Angle in a Pure Shear Problem with the XFEM Method
VM288 - Electrical Input Admittance on a Piezoelectric Transducer Using the Enforced Motion Approach
VM289 - Pressurized Spherical Cavity in an Infinite Medium with Perfectly Matched Layers (PML)
VM290 - Pressurized Spherical Cavity in an Infinite Medium Using Infinite Elements
VM291 - Force on the Boundary of a Semi-Infinite Body (Boussinesq Problem)
VM292 - Interference Fit Between Two Cylinders
VM293 - Evaluation of Stress Intensity Factor KI Using the Unstructured Mesh Method (UMM)
II. Benchmark Study Descriptions
1. Overview
1.1. Description of the Benchmark Studies
1.2. Benchmark Test Case Content and Nomenclature
1.3. Running the Benchmark Test Cases
1.4. Energy Norm
1.5. Benchmark Test Case Coverage Index
Benchmark C1 - Built-In Plate Under Uniformly Distributed Load
Benchmark C2 - Elliptic Membrane Under a Uniformly Load
Benchmark C3 - Barrel Vault Roof Under Self Weight
Benchmark C4 - Simply-Supported Thin Annular Plate
Benchmark C5 - Simply-Supported Solid Square Plate
Benchmark C6 - 2-D Heat Transfer With Convection
Benchmark C7 - One-Dimensional Transient Heat Transfer
Benchmark C8 - Aluminum Bar Impacting a Rigid Boundary
Benchmark D1 - Straight Cantilever Beam Under Unit Load
Benchmark D2 - Barrel Vault Roof Under Self Weight
Benchmark D3 - Free-Free Vibration of a Solid Beam
III. ANSYS LS-DYNA Study Descriptions
1. ANSYS LS-DYNA Study Overview
VME1 - Response of Spring-Mass System to Step Input
VME2 - Drop Analysis of a Block Onto a Spring Scale
VME3 - Response of Spring-Mass-Damper System
VME4 - Undamped Vibration Absorber
VME5 - Pinned Bar Under Gravity Loading
VME6 - Projectile with Air Resistance
IV. NAFEMS Benchmarks
1. NAFEMS Benchmarks Overview
VMFEBSTA-LE1 - Linear Elastic Analysis on an Elliptical Membrane
VMFEBSTA-LE5 - Linear Elastic Analysis on a Z-Section Cantilevered Plate
VMLSB2-LE8 - Linear Elastic Axisymmetric Shell with Pressure Loading
VMLSB2-LE9 - Linear Elastic Axisymmetric Branched Shell with Pressure Loading
VMLSB2-LE11 - Linear Elastic Axisymmetric Shell with Pressure Loading
VMP09-T2 - Pin-Ended Double Cross: In-Plane Vibration
VMP09-T4 - Cantilever with Off-Center Point Masses
VMP09-T5 - Deep Simply-Supported Beam
VMP09-T12 - Free Thin Square Plate
VMP09-T15 - Clamped Thin Rhombic Plate
VMP09-T33 - Free Annular Membrane
VMP09-T52 - Simply-Supported 'Solid' Square Plate
VMR020-t1a - Center Cracked Plate in Tension
VMR020-t1b - Center Cracked Plate with Quadratic Thermal Distribution
VMR020-t2a - Single Edge Cracked Plate Subjected to Uniform Tensile Stress
VMR020-t2b - Single Edge Cracked Plate Subjected to Uniform Normal Displacement
VMR020-t3a - An Angle Crack Embedded in a Plate Subjected to Uniaxial Tension
VMR020-t3b - An Angle Crack Embedded in a Plate Subjected to Uniaxial Tension
VMR020-t3c - An Angle Crack Embedded in a Plate Subjected to Uniaxial Tension
VMR020-t4a - Crack at a Hole in a Plate Subjected to Uniaxial Tension
VMR020-t4b - Crack at a Hole in a Plate Subjected to Uniaxial Tension
VMR020-t5 - Axisymmetric Crack in a Bar
VMR020-t6 - Compact Tension Specimen
VMR020-t8a - V-Notch Cracked Plate Subjected to Uniform Tensile Stress
VMR020-t8b - V-Notch Cracked Plate Subjected to Uniform Normal Displacement
VMR027-3A - 2-D Plane Stress - Biaxial (negative) Load Secondary Creep
VMR027-3B - 2-D Plane Stress - Biaxial (negative) Displacement Secondary Creep
VMR027-4C - 2-D Plane Stress - Shear Loading Secondary Creep
VMR027-5B - 2-D Plane Strain - Biaxial Displacement Secondary Creep
VMR027-6B - 3-D - Triaxial Displacement Secondary Creep
VMR027-10A - 2-D Plane Stress - Biaxial (negative) Load Primary Creep
VMR027-10B - 2-D Plane Stress - Biaxial (negative) Displacement Primary Creep
VMR027-10C - 2-D Plane Stress - Biaxial (negative) Stepped Load - Primary Creep
VMR027-12B - 2-D Plane Stress - Uniaxial Displacement Primary-Secondary Creep
VMR027-12C - 2-D Plane Stress - Stepped Load Primary - Secondary Creep
VMR029-T1 - Elastic Large Deflection Response of a Z-Shaped Cantilever Upper End Load
VMR029-T4 - Lateral Torsional Buckling of an Elastic Cantilever Subjected to Transverse End Load
VMR029-T5 - Large deflection of a curved elastic cantilever under transverse end load
VMR029-T7 - Large Displacement of a Hinged Spherical Shell under Uniform Pressure Loading
VMR029-T9 - Large Elastic Deflection of a Pinched Hemispherical Shell
VMR031-T1 - Laminated Strip under Three-Point Bending
VMR031-T2 - Wrapped Thick Cylinder under Pressure and Thermal Loading
VMR031-T3 - Three-Layer Sandwich Shell under Normal Pressure Loading
VMR038-2A - J Integral Value for Centered Crack Plate with BISO Material Model
VMR038-2B - J Integral Value for Centered Crack Plate with Elastic Perfectly Plastic Material
VMR038-2E - J Integral Value for Centered Crack Plate with Elastic Perfectly Plastic Material
VMR038-2g - Centered Crack Plate Ender Thermal Loading with Elastic Perfectly Plastic Material
VMR038-3A - J integral value for compact tension specimen with BISO material model
VMR038-4A - J Integral Value for Three Point Bend Specimen with Power Law Hardening
VMR049-CR1 - Constant-Load Creep Benchmark
VMR049-CR2 - Constant-Displacement Creep Benchmark
VMR049-CR3 - Variable-Load Uniaxial Creep Benchmark
VMR049-CR4 - Pressurised Cylinder Creep Benchmark
VMR049-CR5 - Torsional Creep of Square Shaft
VMR049-CR6 - Thermally Induced Creep Benchmark
VMR049-PL1 - 2D Plane Strain Plasticity Benchmark
VMR049-PL2 - 2D Plane Stress Plasticity Benchmark
VMR049-PL3 - 3D Plasticity Benchmark
VMR049-PL5 - Pressurised Cylinder Plasticity Benchmark
VMR083-CA1 - Sound Radiation of a Vibrating Sphere
VMR083-CA2 - Sound Radiation of a Cylinder with Vibrating Lateral Surface
V. NRC Piping Benchmarks
1. NRC Piping Benchmarks Overview
1.1. Piping Benchmarks using Archived Elements
1.2. Piping Benchmarks using Current Technology Elements
1.3. Demonstration Problem 1
1.4. Demonstration Problem 2
1.5. Demonstration Problem 3
VM-NR1677-01-1-a - NUREG/CR-1677: Volume 1, Benchmark Problem No. 1
VM-NR1677-01-2-a - NUREG/CR-1677: Volume 1, Benchmark Problem No. 2
VM-NR1677-01-3-a - NUREG/CR-1677: Volume 1, Benchmark Problem No. 3
VM-NR1677-01-4-a - NUREG/CR-1677: Volume 1, Benchmark Problem No. 4
VM-NR1677-01-5-a - NUREG/CR-1677: Volume 1, Benchmark Problem No. 5
VM-NR1677-01-6-a - NUREG/CR-1677: Volume 1, Benchmark Problem No. 6
VM-NR1677-01-7-a - NUREG/CR-1677: Volume 1, Benchmark Problem No. 7
VM-NR1677-02-1-a - NUREG/CR-1677: Volume 2, Benchmark Problem No. 1
VM-NR1677-02-2-a - NUREG/CR-1677: Volume 2, Benchmark Problem No. 2
VM-NR1677-02-3-a - NUREG/CR-1677: Volume 2, Benchmark Problem No. 3
VM-NR1677-02-4-a - NUREG/CR-1677: Volume 2, Benchmark Problem No. 4
VM-NR6645-01-1-a - VM-NR6645-01-1-a
VM-NR1677-01-1 - NUREG/CR-1677: Volume 1, Benchmark Problem No. 1
VM-NR1677-01-2 - NUREG/CR-1677: Volume 1, Benchmark Problem No. 2
VM-NR1677-01-3 - NUREG/CR-1677: Volume 1, Benchmark Problem No. 3
VM-NR1677-01-4 - NUREG/CR-1677: Volume 1, Benchmark Problem No. 4
VM-NR1677-01-5 - NUREG/CR-1677: Volume 1, Benchmark Problem No. 5
VM-NR1677-01-6 - NUREG/CR-1677: Volume 1, Benchmark Problem No. 6
VM-NR1677-01-7 - NUREG/CR-1677: Volume 1, Benchmark Problem No. 7
VM-NR1677-02-1 - NUREG/CR-1677: Volume 2, Benchmark Problem No. 1
VM-NR1677-02-2 - NUREG/CR-1677: Volume 2, Benchmark Problem No. 2
VM-NR1677-02-3 - NUREG/CR-1677: Volume 2, Benchmark Problem No. 3
VM-NR1677-02-4 - NUREG/CR-1677: Volume 2, Benchmark Problem No. 4
VM-NR6645-01-1 - NUREG/CR-6645-01-1
A. Verification Test Case Input Listings
A.1. VM1 Input Listing
A.2. VM2 Input Listing
A.3. VM3 Input Listing
A.4. VM4 Input Listing
A.5. VM5 Input Listing
A.6. VM6 Input Listing
A.7. VM7 Input Listing
A.8. VM8 Input Listing
A.9. VM9 Input Listing
A.10. VM10 Input Listing
A.11. VM11 Input Listing
A.12. VM12 Input Listing
A.13. VM13 Input Listing
A.14. VM14 Input Listing
A.15. VM15 Input Listing
A.16. VM16 Input Listing
A.17. VM17 Input Listing
A.18. VM18 Input Listing
A.19. VM19 Input Listing
A.20. VM20 Input Listing
A.21. VM21 Input Listing
A.22. VM22 Input Listing
A.23. VM23 Input Listing
A.24. VM24 Input Listing
A.25. VM25 Input Listing
A.26. VM26 Input Listing
A.27. VM27 Input Listing
A.28. VM28 Input Listing
A.29. VM29 Input Listing
A.30. VM30 Input Listing
A.31. VM31 Input Listing
A.32. VM32 Input Listing
A.33. VM33 Input Listing
A.34. VM34 Input Listing
A.35. VM35 Input Listing
A.36. VM36 Input Listing
A.37. VM37 Input Listing
A.38. VM38 Input Listing
A.39. VM39 Input Listing
A.40. VM40 Input Listing
A.41. VM41 Input Listing
A.42. VM42 Input Listing
A.43. VM43 Input Listing
A.44. VM44 Input Listing
A.45. VM45 Input Listing
A.46. VM46 Input Listing
A.47. VM47 Input Listing
A.48. VM48 Input Listing
A.49. VM49 Input Listing
A.50. VM50 Input Listing
A.51. VM51 Input Listing
A.52. VM52 Input Listing
A.53. VM53 Input Listing
A.54. VM54 Input Listing
A.55. VM55 Input Listing
A.56. VM56 Input Listing
A.57. VM57 Input Listing
A.58. VM58 Input Listing
A.59. VM59 Input Listing
A.60. VM60 Input Listing
A.61. VM61 Input Listing
A.62. VM62 Input Listing
A.63. VM63 Input Listing
A.64. VM64 Input Listing
A.65. VM65 Input Listing
A.66. VM66 Input Listing
A.67. VM67 Input Listing
A.68. VM68 Input Listing
A.69. VM69 Input Listing
A.70. VM70 Input Listing
A.71. VM71 Input Listing
A.72. VM72 Input Listing
A.73. VM73 Input Listing
A.74. VM74 Input Listing
A.75. VM75 Input Listing
A.76. VM76 Input Listing
A.77. VM77 Input Listing
A.78. VM78 Input Listing
A.79. VM79 Input Listing
A.80. VM80 Input Listing
A.81. VM81 Input Listing
A.82. VM82 Input Listing
A.83. VM83 Input Listing
A.84. VM84 Input Listing
A.85. VM85 Input Listing
A.86. VM86 Input Listing
A.87. VM87 Input Listing
A.88. VM88 Input Listing
A.89. VM89 Input Listing
A.90. VM90 Input Listing
A.91. VM91 Input Listing
A.92. VM92 Input Listing
A.93. VM93 Input Listing
A.94. VM94 Input Listing
A.95. VM95 Input Listing
A.96. VM96 Input Listing
A.97. VM97 Input Listing
A.98. VM98 Input Listing
A.99. VM99 Input Listing
A.100. VM100 Input Listing
A.101. VM101 Input Listing
A.102. VM102 Input Listing
A.103. VM103 Input Listing
A.104. VM104 Input Listing
A.105. VM105 Input Listing
A.106. VM106 Input Listing
A.107. VM107 Input Listing
A.108. VM108 Input Listing
A.109. VM109 Input Listing
A.110. VM110 Input Listing
A.111. VM111 Input Listing
A.112. VM112 Input Listing
A.113. VM113 Input Listing
A.114. VM114 Input Listing
A.115. VM115 Input Listing
A.116. VM116 Input Listing
A.117. VM117 Input Listing
A.118. VM118 Input Listing
A.119. VM119 Input Listing
A.120. VM120 Input Listing
A.121. VM121 Input Listing
A.122. VM122 Input Listing
A.123. VM123 Input Listing
A.124. VM124 Input Listing
A.125. VM125 Input Listing
A.126. VM126 Input Listing
A.127. VM127 Input Listing
A.128. VM128 Input Listing
A.129. VM129 Input Listing
A.130. VM130 Input Listing
A.131. VM131 Input Listing
A.132. VM132 Input Listing
A.133. VM133 Input Listing
A.134. VM134 Input Listing
A.135. VM135 Input Listing
A.136. VM136 Input Listing
A.137. VM137 Input Listing
A.138. VM138 Input Listing
A.139. VM139 Input Listing
A.140. VM140 Input Listing
A.141. VM141 Input Listing
A.142. VM142 Input Listing
A.143. VM143 Input Listing
A.144. VM144 Input Listing
A.145. VM145 Input Listing
A.146. VM146 Input Listing
A.147. VM147 Input Listing
A.148. VM148 Input Listing
A.149. VM149 Input Listing
A.150. VM150 Input Listing
A.151. VM151 Input Listing
A.152. VM152 Input Listing
A.153. VM153 Input Listing
A.154. VM154 Input Listing
A.155. VM155 Input Listing
A.156. VM156 Input Listing
A.157. VM157 Input Listing
A.158. VM158 Input Listing
A.159. VM159 Input Listing
A.160. VM160 Input Listing
A.161. VM161 Input Listing
A.162. VM162 Input Listing
A.163. VM163 Input Listing
A.164. VM164 Input Listing
A.165. VM165 Input Listing
A.166. VM166 Input Listing
A.167. VM167 Input Listing
A.168. VM168 Input Listing
A.169. VM169 Input Listing
A.170. VM170 Input Listing
A.171. VM171 Input Listing
A.172. VM172 Input Listing
A.173. VM173 Input Listing
A.174. VM174 Input Listing
A.175. VM175 Input Listing
A.176. VM176 Input Listing
A.177. VM177 Input Listing
A.178. VM178 Input Listing
A.179. VM179 Input Listing
A.180. VM180 Input Listing
A.181. VM181 Input Listing
A.182. VM182 Input Listing
A.183. VM183 Input Listing
A.184. VM184 Input Listing
A.185. VM185 Input Listing
A.186. VM186 Input Listing
A.187. VM187 Input Listing
A.188. VM188 Input Listing
A.189. VM189 Input Listing
A.190. VM190 Input Listing
A.191. VM191 Input Listing
A.192. VM192 Input Listing
A.193. VM193 Input Listing
A.194. VM194 Input Listing
A.195. VM195 Input Listing
A.196. VM196 Input Listing
A.197. VM197 Input Listing
A.198. VM198 Input Listing
A.199. VM199 Input Listing
A.200. VM200 Input Listing
A.201. VM201 Input Listing
A.202. VM202 Input Listing
A.203. VM203 Input Listing
A.204. VM204 Input Listing
A.205. VM205 Input Listing
A.206. VM206 Input Listing
A.207. VM207 Input Listing
A.208. VM208 Input Listing
A.209. VM209 Input Listing
A.210. VM210 Input Listing
A.211. VM211 Input Listing
A.212. VM212 Input Listing
A.213. VM213 Input Listing
A.214. VM214 Input Listing
A.215. VM215 Input Listing
A.216. VM216 Input Listing
A.217. VM217 Input Listing
A.218. VM218 Input Listing
A.219. VM219 Input Listing
A.220. VM220 Input Listing
A.221. VM221 Input Listing
A.222. VM222 Input Listing
A.223. VM223 Input Listing
A.224. VM224 Input Listing
A.225. VM225 Input Listing
A.226. VM226 Input Listing
A.227. VM227 Input Listing
A.228. VM228 Input Listing
A.229. VM229 Input Listing
A.230. VM230 Input Listing
A.231. VM231 Input Listing
A.232. VM232 Input Listing
A.233. VM233 Input Listing
A.234. VM234 Input Listing
A.235. VM235 Input Listing
A.236. VM236 Input Listing
A.237. VM237 Input Listing
A.238. VM238 Input Listing
A.239. VM239 Input Listing
A.240. VM240 Input Listing
A.241. VM241 Input Listing
A.242. VM242 Input Listing
A.243. VM243 Input Listing
A.244. VM244 Input Listing
A.245. VM245 Input Listing
A.246. VM246 Input Listing
A.247. VM247 Input Listing
A.248. VM248 Input Listing
A.249. VM249 Input Listing
A.250. VM250 Input Listing
A.251. VM251 Input Listing
A.252. VM252 Input Listing
A.253. VM253 Input Listing
A.254. VM254 Input Listing
A.255. VM255 Input Listing
A.256. VM256 Input Listing
A.257. VM257 Input Listing
A.258. VM258 Input Listing
A.259. VM259 Input Listing
A.260. VM260 Input Listing
A.261. VM261 Input Listing
A.262. VM262 Input Listing
A.263. VM263 Input Listing
A.264. VM264 Input Listing
A.265. VM265 Input Listing
A.266. VM266 Input Listing
A.267. VM267 Input Listing
A.268. VM268 Input Listing
A.269. VM269 Input Listing
A.270. VM270 Input Listing
A.271. VM271 Input Listing
A.272. VM272 Input Listing
A.273. VM273 Input Listing
A.274. VM274 Input Listing
A.275. VM275 Input Listing
A.276. VM276 Input Listing
A.277. VM277 Input Listing
A.278. VM278 Input Listing
A.279. VM279 Input Listing
A.280. VM280 Input Listing
A.281. VM281 Input Listing
A.282. VM282 Input Listing
A.283. VM283 Input Listing
A.284. VM284 Input Listing
A.285. VM285 Input Listing
A.286. VM286 Input Listing
A.287. VM287 Input Listing
A.288. VM288 Input Listing
A.289. VM289 Input Listing
A.290. VM290 Input Listing
A.291. VM291 Input Listing
A.292. VM292 Input Listing
A.293. VM293 Input Listing
B. Benchmark Input Listings
B.1. Benchmark C1 Input Listing
B.2. Benchmark C2 Input Listing
B.3. Benchmark C3 Input Listing
B.4. Benchmark C4 Input Listing
B.5. Benchmark C5 Input Listing
B.6. Benchmark C6 Input Listing
B.7. Benchmark C7 Input Listing
B.8. Benchmark C8 Input Listing
B.9. Benchmark D1 Input Listing
B.10. Benchmark D2 Input Listing
B.11. Benchmark D3 Input Listing
C. ANSYS LS-DYNA Input Listings
C.1. VME1 Input Listing
C.2. VME2 Input Listing
C.3. VME3 Input Listing
C.4. VME4 Input Listing
C.5. VME5 Input Listing
C.6. VME6 Input Listing
D. NAFEMS Input Listings
D.1. VM-P09-t2 188 Input Listing
D.2. VM-P09-t2 189 Input Listing
D.3. VM-P09-t4 188 Input Listing
D.4. VM-P09-t4 189 Input Listing
D.5. VM-P09-t5 188 Input Listing
D.6. VM-P09-t5 189 Input Listing
D.7. VM-P09-t12 181 Input Listing
D.8. VM-P09-t12 281 Input Listing
D.9. VM-P09-t15 181 Input Listing
D.10. VM-P09-t15 281 Input Listing
D.11. VM-P09-t33 182 Input Listing
D.12. VM-P09-t33 183 Input Listing
D.13. VM-P09-t52 181 Input Listing
D.14. VM-P09-t52 185 Input Listing
D.15. VM-P09-t52 186 Input Listing
D.16. VM-P09-t52 187 Input Listing
D.17. VM-P09-t52 281 Input Listing
D.18. VM-R020-t1a 183 Input Listing
D.19. VM-R020-t1b 183 Input Listing
D.20. VM-R020-t2a 183 Input Listing
D.21. VM-R020-t2b 183 Input Listing
D.22. VM-R020-t3a 183 Input Listing
D.23. VM-R020-t3b 183 Input Listing
D.24. VM-R020-t3c 183 Input Listing
D.25. VM-R020-t4a 183 Input Listing
D.26. VM-R020-t4b 183 Input Listing
D.27. VM-R020-t5a 183 Input Listing
D.28. VM-R020-t6a 183 Input Listing
D.29. VM-R020-t8a 183 Input Listing
D.30. VM-R020-t8b 183 Input Listing
D.31. VM-R027-3A 181 Input Listing
D.32. VM-R027-3A 182 Input Listing
D.33. VM-R027-3A 183 Input Listing
D.34. VM-R027-3A 281 Input Listing
D.35. VM-R027-3B 181 Input Listing
D.36. VM-R027-3B 182 Input Listing
D.37. VM-R027-3B 183 Input Listing
D.38. VM-R027-3B 281 Input Listing
D.39. VM-R027-4C 181 Input Listing
D.40. VM-R027-4C 182 Input Listing
D.41. VM-R027-4C 183 Input Listing
D.42. VM-R027-4C 281 Input Listing
D.43. VM-R027-5B 182 Input Listing
D.44. VM-R027-5B 183 Input Listing
D.45. VM-R027-6B 185 Input Listing
D.46. VM-R027-6B 186 Input Listing
D.47. VM-R027-6B 187 Input Listing
D.48. VM-R027-10A 181 Input Listing
D.49. VM-R027-10A 182 Input Listing
D.50. VM-R027-10A 183 Input Listing
D.51. VM-R027-10A 281 Input Listing
D.52. VM-R027-10B 181 Input Listing
D.53. VM-R027-10B 182 Input Listing
D.54. VM-R027-10B 183 Input Listing
D.55. VM-R027-10B 281 Input Listing
D.56. VM-R027-10C 181 Input Listing
D.57. VM-R027-10C 182 Input Listing
D.58. VM-R027-10C 183 Input Listing
D.59. VM-R027-10C 281 Input Listing
D.60. VM-R027-12B 181 Input Listing
D.61. VM-R027-12B 182 Input Listing
D.62. VM-R027-12B 183 Input Listing
D.63. VM-R027-12B 281 Input Listing
D.64. VM-R027-12C 181 Input Listing
D.65. VM-R027-12C 182 Input Listing
D.66. VM-R027-12C 183 Input Listing
D.67. VM-R027-12C 281 Input Listing
D.68. VM-R029-T1 181 Input Listing
D.69. VM-R029-T1 185 Input Listing
D.70. VM-R029-T1 188 Input Listing
D.71. VM-R029-T1 189 Input Listing
D.72. VM-R029-T1 190 Input Listing
D.73. VM-R029-T1 281 Input Listing
D.74. VM-R029-T4 181 Input Listing
D.75. VM-R029-T4 185 Input Listing
D.76. VM-R029-T4 188 Input Listing
D.77. VM-R029-T4 189 Input Listing
D.78. VM-R029-T4 190 Input Listing
D.79. VM-R029-T4 281 Input Listing
D.80. VM-R029-T5 185 Input Listing
D.81. VM-R029-T5 188 Input Listing
D.82. VM-R029-T5 189 Input Listing
D.83. VM-R029-T5 190 Input Listing
D.84. VM-R029-T7 181 Input Listing
D.85. VM-R029-T7 185 Input Listing
D.86. VM-R029-T7 190 Input Listing
D.87. VM-R029-T7 281 Input Listing
D.88. VM-R029-T9 181 Input Listing
D.89. VM-R029-T9 185 Input Listing
D.90. VM-R029-T9 190 Input Listing
D.91. VM-R029-T9 281 Input Listing
D.92. VMR031-T1 281 Input Listing
D.93. VMR031-T2 281 Input Listing
D.94. VMR031-T3 181 Input Listing
D.95. VMR031-T3 281 Input Listing
D.96. VMR038-2A 182 Input Listing
D.97. VMR038-2A 183 Input Listing
D.98. VMR038-2B 182 Input Listing
D.99. VMR038-2B 183 Input Listing
D.100. VMR038-2E 182 Input Listing
D.101. VMR038-2g 182 Input Listing
D.102. VMR038-3A 182 Input Listing
D.103. VMR038-3A 183 Input Listing
D.104. VMR038-4A 182 Input Listing
D.105. VMR038-4A 183 Input Listing
D.106. VMLSB2-LE8 208 Input Listing
D.107. VMLSB2-LE8 209 Input Listing
D.108. VMLSB2-LE9 208 Input Listing
D.109. VMLSB2-LE9 209 Input Listing
D.110. VMLSB2-LE11 185 Input Listing
D.111. VMLSB2-LE11 186 Input Listing
D.112. VM-R049-1A 181 Input Listing
D.113. VM-R049-1A 182 Input Listing
D.114. VM-R049-1A 183 Input Listing
D.115. VM-R049-1A 281 Input Listing
D.116. VM-R049-1B 181 Input Listing
D.117. VM-R049-1B 182 Input Listing
D.118. VM-R049-1B 183 Input Listing
D.119. VM-R049-1B 281 Input Listing
D.120. VM-R049-1C 181 Input Listing
D.121. VM-R049-1C 182 Input Listing
D.122. VM-R049-1C 183 Input Listing
D.123. VM-R049-1C 281 Input Listing
D.124. VM-R049-2 181 Input Listing
D.125. VM-R049-2 182 Input Listing
D.126. VM-R049-2 183 Input Listing
D.127. VM-R049-2 185 Input Listing
D.128. VM-R049-2 187 Input Listing
D.129. VM-R049-2 281 Input Listing
D.130. VM-R049-3 181 Input Listing
D.131. VM-R049-3 182 Input Listing
D.132. VM-R049-3 183 Input Listing
D.133. VM-R049-3 281 Input Listing
D.134. VM-R049-4 182 Input Listing
D.135. VM-R049-4 183 Input Listing
D.136. VM-R049-5 185 Input Listing
D.137. VM-R049-5 186 Input Listing
D.138. VM-R049-5 187 Input Listing
D.139. VM-R049-6 182 Input Listing
D.140. VM-R049-6 183 Input Listing
D.141. VM-R049-PL1A 182 Input Listing
D.142. VM-R049-PL1A 183 Input Listing
D.143. VM-R049-PL1B 182 Input Listing
D.144. VM-R049-PL1B 183 Input Listing
D.145. VM-R049-PL2A 181 Input Listing
D.146. VM-R049-PL2A 182 Input Listing
D.147. VM-R049-PL2A 183 Input Listing
D.148. VM-R049-PL2A 281 Input Listing
D.149. VM-R049-PL2B 181 Input Listing
D.150. VM-R049-PL2B 182 Input Listing
D.151. VM-R049-PL2B 281 Input Listing
D.152. VM-R049-PL3A 185 Input Listing
D.153. VM-R049-PL3A 186 Input Listing
D.154. VM-R049-PL3A 187 Input Listing
D.155. VM-R049-PL3B 185 Input Listing
D.156. VM-R049-PL3B 186 Input Listing
D.157. VM-R049-PL3B 187 Input Listing
D.158. VM-R049-PL3B 190 Input Listing
D.159. VM-R049-PL5A 182 Input Listing
D.160. VM-R049-PL5A 183 Input Listing
D.161. VM-R049-PL5B 182 Input Listing
D.162. VM-R049-PL5B 183 Input Listing
D.163. VM-R083-CA1 221 Input Listing
D.164. VM-R083-CA2 221 Input Listing
D.165. VMFEBSTA-LE1 181 Input Listing
D.166. VMFEBSTA-LE5 181 Input Listing
D.167. VMFEBSTA-LE5 281 Input Listing
E. NRC Piping Benchmarks Input Listings
E.1. vm-nr1677-1-1a-a Input Listing
E.2. vm-nr1677-1-2a-a Input Listing
E.3. vm-nr1677-1-3a-a Input Listing
E.4. vm-nr1677-1-4a-a Input Listing
E.5. vm-nr1677-1-5a-a Input Listing
E.6. vm-nr1677-1-6a-a Input Listing
E.7. vm-nr1677-1-7a-a Input Listing
E.8. vm-nr1677-2-1a-a Input Listing
E.9. vm-nr1677-2-1b-a Input Listing
E.10. vm-nr1677-2-1c-a Input Listing
E.11. vm-nr1677-2-2a-a Input Listing
E.12. vm-nr1677-2-2b-a Input Listing
E.13. vm-nr1677-2-2c-a Input Listing
E.14. vm-nr1677-2-3a-a Input Listing
E.15. vm-nr1677-2-3b-a Input Listing
E.16. vm-nr1677-2-3c-a Input Listing
E.17. vm-nr1677-2-4a-a Input Listing
E.18. vm-nr1677-2-4c-a Input Listing
E.19. vm-nr6645-1-1a-a Input Listing
E.20. vm-nr6645-1-2a-a Input Listing
E.21. vm-nr1677-01-1a Input Listing
E.22. vm-nr1677-01-2a Input Listing
E.23. vm-nr1677-01-3a Input Listing
E.24. vm-nr1677-01-4a Input Listing
E.25. vm-nr1677-01-5a Input Listing
E.26. vm-nr1677-01-6a Input Listing
E.27. vm-nr1677-01-7a Input Listing
E.28. vm-nr1677-02-1a Input Listing
E.29. vm-nr1677-02-1b Input Listing
E.30. vm-nr1677-02-1c Input Listing
E.31. vm-nr1677-02-2a Input Listing
E.32. vm-nr1677-02-2b Input Listing
E.33. vm-nr1677-02-2c Input Listing
E.34. vm-nr1677-02-3a Input Listing
E.35. vm-nr1677-02-3b Input Listing
E.36. vm-nr1677-02-3c Input Listing
E.37. vm-nr6645-01-1a Input Listing
E.38. vm-nr6645-01-2a Input Listing
E.39. vm-nr1677-02-4a Input Listing
E.40. vm-nr1677-02-4c Input Listing
E.41. demonstration-problem1-290 Input Listing
E.42. demonstration-problem1-281 Input Listing
E.43. demonstration-problem1-18 Input Listing
E.44. demonstration-problem2-290 Input Listing
E.45. demonstration-problem2-281 Input Listing
E.46. demonstration-problem2-16-18 Input Listing
E.47. demonstration_problem3-289-290 Input Listing
E.48. demonstration-problem3-281 Input Listing
E.49. demonstration-problem3-16-18 Input Listing

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