prepared checked approved Date: Date: Date: S. Fahrendholz/R.Geiger Dr.-Ing. Jürgen Bellmann Dr.-Ing.

Transcription

1 Verification Manual Version prepared checked approved Date: Date: Date: S. Fahrendholz/R.Geiger Dr.Ing. Jürgen Bellmann Dr.Ing. Casimir Katz Document name: q:\dok\qs\verification.doc SOFiSTiK Verification Manual 1

2 Table of Content 1 Quality Certification Developement and Production Reporting of Bugs and Software Enhancements Validation Test No IC1 Tapered Membrane End Load Test No IC2 Tapered Membrane Gravity Load Test NO IC3 Tapered Membrane Edge Shear Test No IC4 Tapered Membrane Gravity Load Test No IC5 Circular Membrane Edge Pressure Test No IC6 Circular Membrane Point Load Test No IC7 Cicular Membrane Parabolic Temperature Test No IC8 Shear Diffusion Test No IC9 Elliptic Membrane Test No IC10 Tapered Plate Edge Shear Test No IC11 Tapered Plate Gravity Test No IC12 Elliptic Plate Normal Pressure Test No IC13 Skew Plate Normal Pressure Test No IC14 Tapered Thick Shell Pressure Load Test No IC15 Tapered Thick Shell Selfweight Test No IC16 CylinderTaperSphere Temperature Test No IC17 Hemisphere External Pressure Test No IC18 Hemisphere Point Load Test No IC19 Cylindrical Shell Edge Moment Test No IC24 Catenoidal Shell Internal Pressure Test No IC27 Cylinder/Sphere Internal Pressure Test No IC28 Circular Paraboloid Gravity Test No IC29 ZSection Cantilever Torsion Bending Test No IC30 ZSection Cantilever Beam Bending Test No IC31 Axisymmetric Hyperbolic Shell Edge Loading Test No IC32 Axisymmetric Hyperbolic Shell Pressure Test No IC34 Axisymmetric Catenoidal Shell Pressure Test No IC37 Axisymmetric Stiffened Cylinder Pressure Test No IC38 Axisymmetric Cylinder/Sphere Pressurre Test No IC39 Axisymmetric Cylinder/Sphere Pressure Test 5 Fundamental 2D Plasticity Benchmark Test 5 "Dynamic for Deep SimplySupported Beam" Test 5H "Harmonic Forced Vibration Response" Test 5P "Periodic Forced Vibration Response Test 5T "Transient Forced Vibration Response" Literature SOFiSTiK Verification Manual 2

3 1 Quality Certification SOFiSTiK Software is continuously developed since 1981 and used by over customers. To assure the highest quality for our customers we have installed a quality assurance system with the following steps. 1.1 Developement and Production Each new software feature is thoroughly validated by a team of developers, supporters and external customers. A set of reference examples is thus created and documented (partly in German) During the life time of the software questions arising are treated by an intense discussion with customers, authorities and scientists to find the best interpretation. For each minor release of the software (or at least once per month) an automatic comparison of the current results with the reference examples is performed to detect any deviations introduced by other bug fixes. These so called "current versions" are available for all customers with an automatic procedure via Internet. (SONAR) This assures that most bugs will be detected at an early stage. Fast fixes of the software are published as separate betaversions. Once a year a QSRelease is published on CD/DVD. A period of approximately three months is foreseen to assure the actuality of the manuals, online help and to validate the overall consistency of the total software environment. The reference examples are tested on all major targets (i.e. Linux, Windows). These Versions are shipped to all customers. At most every two years we allow for a general new release with changes in the basic structure of the software (e.g. 16 to 32 Bit, or DOS to Windows or a change of the used compiler versions) 1.2 Reporting of Bugs and Software Enhancements Each request from our customers is traced with an helpdesk system assuring that no problem will be lost. All bug fixes or enhancements of the software are documented with version number and date in html files associated to every program module. Serious bugs will be announced to our customers via if the have registered to our news letter. There is also a forum on the internet / or ww.sofistik.com to discuss latest developments and analysis techniques. Although this procedure has minimized the number of errors in the Software, SOFiSTiK can not assure that their software is bugfree or that it will solve a particular problem in a way which is concluding with the opinion of the user in all details. We strongly recommend therefore to use the engineering skill when evaluating the results of any software. 1.3 Insurance SOFiSTiK is Member of the German Association of Consulting Engineers (VBI) and has an professional indemnity insurance. SOFiSTiK Verification Manual 3

4 2 Validation The tasks covered by SOFiSTiK Software are so large, that it is not possible to validate all specific features with known reference solutions. Thus there are variant sources of validation: Internal verification examples for white box testing maintained by the programmer and not generally available to the public. The examples in the manuals wiil show the general behaviour of the program and will give expected or approved results for comparison. The lections given at the annual user meeting of SOFiSTiK (since 1988) show the practical usage of the software within a wide range of applications and the scientific background. Externally established examples. As SOFiSTiK is a member of the NAFEMS ( we have taken most of the examples of the NAFEMS Benchmarks, which follow on the next pages. These are: P07 Linear Static Benchmarks Vol. 1 Hitchings P08 Linear Static Benchmarks Vol. 2 Hitchings R0016 Selected Benchmarks for forced vibration Maguire et. al. R0026 Selected Benchmarks for Material Linken nonlinearity SOFiSTiK Verification Manual 4

5 2.1 Test No IC1 Tapered Membrane End Load Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Edge compression, Line load In this test the simple disk system, depicted above, is analysed with an end load of 10 MN/m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 6, which then has 64x64 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Sxx in point B. Benchmark value 61.3 MPa (8x8 elements), for an 8node second order and a 16node third order quadelement. The results of the benchmark and the program ASE can be found in the following table: Benchmark (8node quad) ASE Mesh Point A (MPa) Point B (MPa) Point A (MPa) Point B (MPa) Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy 2x x x x x x further results in the DATfile Input file: ic1_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 5

6 2.2 Test No IC2 Tapered Membrane Gravity Load Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Selfweight, Gravitational load In this test the simple disk system, depicted above, is analysed with a selfweight of p=70 kn/m² in the x direction and a gravitational acceleration of 9.81 m/s², whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 6, which then has 64x64 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Sxx in point B. Benchmark value MPa (8x8 elements), for an 8node second order and a 16node third order quadelement. The results of the benchmark and the program ASE can be found in the following table: Benchmark (8node quad) ASE Mesh Point A (MPa) Point B (MPa) Point A (MPa) Point B (MPa) Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy 2x x x x x x further results in the DATfile Input file: ic2_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 6

7 2.3 Test NO IC3 Tapered Membrane Edge Shear Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Shear loading In this test the simple disk system, depicted above, is analysed for a uniform shear load of 100 MPa = kn/m²*0.1 m = kn/m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 6, which then has 64x64 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Sxy in point B. Benchmark value 26.9 MPa (8x8 elements), for a 16node third order quadelement. The results of the benchmark and the program ASE can be found in the following table: Benchmark (8node quad) ASE Mesh Point A (MPa) Point B (MPa) Point A (MPa) Point B (MPa) Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy 2x x x x x x further results in the DATfile Input file: ic3_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 7

8 2.4 Test No IC4 Tapered Membrane Gravity Load Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Selfweight, Gravitational load In this test the simple disk system, depicted above, is analysed with a selfweight of p=70 kn/m² in the ydirection and a gravitational acceleration of 9.81 m/s², whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 6, which then has 64x64 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Sxy in point B. Benchmark value MPa (8x8 elements), for an 8node second order and a 16node third order quadelement. The results of the benchmark and the program ASE can be found in the following table: Benchmark (8node quad) ASE Mesh Point A (MPa) Point B (MPa) Point A (MPa) Point B (MPa) Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy 2x x x x x x further results in the DATfile Input file: ic4_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 8

9 2.5 Test No IC5 Circular Membrane Edge Pressure Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Edge compression, Line load In this test the disk system, depicted above, is analysed with an edge compression of 100 MPa, which is equivalent to a line load of kn/m for a thickness of 0.1 m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. Initially the system is generated with an element mesh consisting of 8x1 quadrilateral elements. Subsequently the number of elements are doubled, up to an element mesh having 64x8 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Syy in point D. Benchmark value 1150 MPa (analytic). The results of the benchmark and the program ASE can be found in the following table: Mesh 8x x2 32x4 Point D (MPa) radius 10m Benchmark Point C (MPa) radius 11m Point D (MPa) radius 10m ASE Point C (MPa) radius 11m Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy x further results in the DATfile Input file: ic5_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 9

10 2.6 Test No IC6 Circular Membrane Point Load Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Point load In this test the disk system, depicted above, is analysed with a point load of 5000 N in radial direction at point B, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. Initially the system is generated with an element mesh consisting of 8x1 quadrilateral elements. Subsequently the number of elements are doubled, up to an element mesh having 64x8 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Syy in point D. Benchmark value 532 MPa (16x2 elements). The results of the benchmark and the program ASE can be found in the following table: Mesh 8x1 16x2 32x4 64x8 Point D (MPa) radius 10m Benchmark Point C (MPa) radius 11m Point D (MPa) radius 10m ASE Point C (MPa) radius 11m Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy further results in the DATfile Input file: ic6_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 10

11 2.7 Test No IC7 Cicular Membrane Parabolic Temperature Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Temperature load In this test the disk system, depicted above, is analysed for a fluctuating temperature load, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. The temperature expansion coefficient is taken as 2.3E4 / C. The linearly fluctuating temperature load, which depends on the radius, was modeled with the program HYDRA. In order to be able to define the maximum temperature load, it is necessary to change the provided element arrangement, so that now the elements are defined having the same size and they are aligned in the radial direction (HYDRA and TALPA can only analyse temperature loads in nodes). The system is generated with element meshes of 4x2, 8x4, 16x8, 32x16 and 64x32 quadelements. The calculation is made with the program TALPA. The GRAFplot shows the temperature loads from HYDRA by means of a coloured diagram. Results: Stress Syy in point A. Theoretical value 115 MPa (analytical), benchmark value 104 MPa (for 8x4 elements according to benchmark method 1). The results of the program TALPA are compared against the benchmark results from method 1. They can be found in the following table: Benchmark TALPA Mesh Point A (MPa) Point A (MPa) Sxx Syy Sxy Sxx Syy Sxy 4x x x x x Theory further results in the DATfile Input file: ic7_e.dat Last changed: Essential programs: HYDRA, TALPA SOFiSTiK Verification Manual 11

12 2.8 Test No IC8 Shear Diffusion Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Truss elements, Point load In this test the disk system, depicted above, is analysed with edge beams and a point load of 10 kn in horizontal direction at point B, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh consisting of 24x2 quadrilateral elements and the respective beam elements (type TRUS). In the subsequent cases the number of elements are doubled, up to case 3 having an element mesh of 96x8 quadrilateral elements. The calculation is made with the program ASE. Results: Shear stress Sxy in point E. Theoretical value 27.8 MPa (analytical), benchmark value 34.3 MPa (24x2 element mesh with 8node elements). The results of the benchmark and the program ASE can be found in the following table: Benchmark ASE Mesh Point E (MPa) Point E (MPa) Sxy Sxy 24x x x Theory 27.8 further results in the DATfile Input file: ic8_e.dat Last changed : Essential programs: ASE SOFiSTiK Verification Manual 12

13 2.9 Test No IC9 Elliptic Membrane Classification: Disk, Steel Index: NAFEMS, Benchmark, Disk, Line load In this test the disk system, depicted above, is analysed with a line load of 1000 kn/m = 10MPa*0.1m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh consisting of 3x2 quadrilateral elements. In case 2 the 3x2 element mesh is subdivided by triangular elements. For case 3 the system consists of 6x4 quadelements, and is respectively subdivided by triangular elements in case 4. The calculation is made with the program ASE. Results: Stress Syy in point D. Theoretical value 92.7 MPa (analytical), benchmark value 90.5 MPa (6x4 quadelements). The results of the benchmark and the program ASE can be found in the following table: Benchmark ASE Mesh Point D (MPa) Point D (MPa) Syy Syy 3x x2 quadelements subdivided by trielements x x4 quadelements subdivided by trielements Theory 92.7 further results in the DATfile Input file: ic9_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 13

14 2.10 Test No IC10 Tapered Plate Edge Shear Classification: Plate, Steel Index: NAFEMS, Benchmark, Plate, Shear loading In this test the simple plate system, depicted above, is analysed with a line load of 10 kn/m acting along the edge DB, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 6, which then has 64x64 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Sxx at the top side of the plate in point B. Benchmark value 14.7 MPa (8x8 elements), for an 8node second order and a 16node third order quadelement. The results of the benchmark and the program ASE can be found in the following table: Benchmark (8node quad) ASE Mesh Point A (MPa) Point B (MPa) Point A (MPa) Point B (MPa) Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy 2x x x x x x further results in the DATfile Input file: ic10_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 14

15 2.11 Test No IC11 Tapered Plate Gravity Classification: Plate, Steel Index: NAFEMS, Benchmark, Plate, Selfweight, Gravitational load In this test the simple plate system, depicted above, is analysed with a selfweight of p=70 kn/m² in the zdirection and a gravitational acceleration of 9.81 m/s², whereby an isotropic material with an E modulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 6, which then has 64x64 quadrilateral elements. The calculation is made with the program ASE. Results: Stress Sxx at the top side of the plate in point B. Benchmark value 26 MPa (8x8 elements), for an 8node second order and a 16node third order quadelement. The results of the benchmark and the program ASE can be found in the following table: Benchmark (8node quad) ASE Mesh Point A (MPa) Point B (MPa) Point A (MPa) Point B (MPa) Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy 2x x x x x x further results in the DATfile Input file: ic11_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 15

16 2.12 Test No IC12 Elliptic Plate Normal Pressure Classification: Plate, Steel Index: NAFEMS, Benchmark, Plate, distributed load In this test the plate system, depicted above, is analysed with a distributed load of 1000 kn/m², whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 3x2 quadrilateral elements. In the subsequent case 2 the number of elements are doubled (6x4 quadrilateral elements). The calculation is made with the program ASE. Results: Stress Syy at the top side of the plate in point D. Analytical value 118 MPa. Benchmark value 158 MPa (6x4 elements) for an 8node element and 177 MPa (6x4 elements) for a 16node element. The results of the benchmark and the program ASE can be found in the following table: Benchmark (8node quad) ASE Mesh Point A (MPa) Point D (MPa) Point A (MPa) Point D (MPa) Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy Sxx Syy Sxy 3x x further results in the DATfile Input file: ic12_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 16

17 2.13 Test No IC13 Skew Plate Normal Pressure Classification: Plate, Steel Index: NAFEMS, Benchmark, Plate, Distributed load In this test the simple plate system, depicted above, is analysed with a distributed load in the zdirection of p= 0.7 kn/m² = 0.7 kpa, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 4, which then has 16x16 quadrilateral elements. The calculation is made with the program ASE. Results: max. principal stress at the under side of the plate for point E. Theoretical value MPa (analytical), benchmark value MPa (8node quadelement). The results of the program ASE are compared against the benchmark results, they can be found in the following table: Benchmark ASE Mesh Point E (MPa) Point E (MPa) P1 P2 P3 P1 P2 P3 2x x x x further results in the DATfile Input file: ic13_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 17

18 2.14 Test No IC14 Tapered Thick Shell Pressure Load Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Edge compression, axisymmetrical state In this test the simple shell system, depicted above, is analysed for an axisymmetrical state, with an edge compression of 100 MPa, which is equivalent to a line load of kn/m for a thickness of 0.1 m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 5, which then has 32x32 quadrilateral elements. The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Results: Stress Szz (Stt) in point C. Benchmark value 237 MPa (8x8 elements). The results of the benchmark and the program TALPA can be found in the following table: Benchmark TALPA Mesh Point B (MPa) Point C (MPa) Point B (MPa) Point C (MPa) Sxx Syy Szz Sxy Sxx Syy Szz Sxy Sxx Syy Szz Sxy Sxx Syy Szz Sxy (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) 2x x x x x further results in the DATfile Input file: ic14_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 18

19 2.15 Test No IC15 Tapered Thick Shell Selfweight Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Selfweight, axisymmetrical state In this test the simple shell system, depicted above, is analysed for an axisymmetrical state, with a selfweight of p=70 kn/m² in the xdirection (benchmark ydirection) and a gravitational acceleration of 9.81 m/s², whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 2x2 quadrilateral elements. In the subsequent cases the number of elements are doubled, up to case 5, which then has 32x32 quadrilateral elements. The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Results: Stress Szz (Stt) in point C. Benchmark value 22.8 KPa (8x8 elements). The results of the benchmark and the program TALPA can be found in the following table: Benchmark TALPA Mesh Point B (KPa) Point C (KPa) Point B (KPa) Point C (KPa) Sxx Syy Szz Sxy Sxx Syy Szz Sxy Sxx Syy Szz Sxy Sxx Syy Szz Sxy (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) 2x x x x x further results in the DATfile Input file: ic15_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 19

20 2.16 Test No IC16 CylinderTaperSphere Temperature Classification: Shell, Steel Index: NAFEMS, Benchmark, cylindrical shell, axisymmetric state In this test the cylindrical shell system, depicted above, is analysed for a fluctuating temperature load, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. The temperature expansion coefficient is taken as 2.3E4 / C. The linearly fluctuating temperature load, which depends on the coordinates, was modeled with the program HYDRA. The system is generated with element meshes of 5x1, 10x2, 20x4 and 40x8 quadelements. The calculation is made with the program TALPA, because only this program is able to analyse an axisymmetrical state. The GRAFplot shows the temperature loads from HYDRA by means of a coloured diagram. Results: Stress Sxx (Syy) in point A. Benchmark value 105 MPa (10x2 elements). The results of the benchmark and the program TALPA can be found in the following table: Benchmark TALPA Mesh Point A (MPa) Point F (MPa) Point A (MPa) Point F (MPa) Sxx Syy Szz Sxy Sxx Syy Szz Sxy Sxx Syy Szz Sxy Sxx Syy Szz Sxy (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) (Syy) (Srr) (Stt) (Sry) 5x x x x further results in the DATfile Input file: ic16_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 20

21 2.17 Test No IC17 Hemisphere External Pressure Classification: Shell, Glas Index: NAFEMS, Benchmark, Shell, Distributed load, Symmetry conditions In this test the shell system, depicted above, is analysed with a distributed load, which acts from the outside, of 1MPa = 1000 kn/m² (print error: see DATfile). For this an isotropic material with an Emodulus of 68.25*10³ MPa and a poisson's ratio of 0.3 is used. The system is generated, so that different element meshes, consisting of quadelements, can be analysed. The following element meshes are analysed: 4x4 elements, 8x8 elements and 16x16 elements. The calculation is made with the program ASE. Results: Radial displacement in point G. Theoretical value mm analytically. Benchmark value mm (coarse mesh, 16node quadelement). The results of the benchmark and the program ASE can be found in the following table: Mesh Deflection in points (mm) A B C D E F G Benchmark 3 element ASE 4x x x further results in the DATfile Input file: ic17_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 21

22 2.18 Test No IC18 Hemisphere Point Load Classification: Shell, Glas Index: NAFEMS, Benchmark, Shell, Point load, Symmetry conditions In this test the shell system, depicted above, is analysed with two point loads, each of 2 kn (acting towards the inside and outside respectively), whereby an isotropic material with an Emodulus of 68.25*10³ MPa and a poisson's ratio of 0.3 are used. The system is generated in such a manner, so as to allow the calculation of several different element meshes consisting of quadelements. The following element meshes are investigated: 4x4 elements, 8x8 elements and 16x16 elements. The calculation is made with the program ASE. Results: xdisplacement for point A. Theoretical value m analytically. Benchmark value m (fine mesh, 8node quadelement). The results of the benchmark and the program ASE can be found in the following table: Mesh Benchmark ASE Deflection in points (m) A B A B ux uz ux uy ux uz ux uy 4x x x Theory further results in the DATfile Input file: ic18_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 22

23 2.19 Test No IC19 Cylindrical Shell Edge Moment Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Point load, Symmetry conditions Short descriptions: In this test the shell system, depicted above, is analysed with a moment loading, which is applied to the edge CD, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. The system is generated, so that an element mesh consisting of 2x2 quadrilateral elements can be calculated. The calculation is made with the program ASE. Results: Stress at the outer top surface for point E. Theoretical value 60.0 MPa analytically. Benchmark value 60.0 MPa. The results of the benchmark and the program ASE can be found in the following table: Mesh Benchmark ASE Point E top Point E bottom Point E top Point E bottom Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) 2x Theory further results in the DATfile Input file: ic19_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 23

24 2.20 Test No IC24 Catenoidal Shell Internal Pressure Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Distributed load In this test the shell system, depicted above, is analysed with a distributed load of 1 MPa = 1000 kn/m², whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. The system is generated in such a manner, so as to allow the calculation of several different element meshes consisting of quadelements. The following element meshes are investigated: 3x3 elements, 6x6 elements and 12x12 elements. The calculation is made with the program ASE. Results: Stress Syy (Saa) at point A. Theoretical value 69.1 MPa analytically. Benchmark value MPa (6x6 element mesh with 8node quadelements). The results of the benchmark and the program ASE can be found in the following table: Mesh Benchmark ASE Point A Point A Sxx (MPa) Syy (MPa) Sxx (MPa) Syy (MPa) (Stt) (Saa) (Stt) (Saa) 3x x x Theory further results in the DATfile Input file: ic24_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 24

25 2.21 Test No IC27 Cylinder/Sphere Internal Pressure Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Distributed load In this test the shell system, depicted above, is analysed with a distributed load of 1 MPa = 1000 kn/m², whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. The system is generated in such a manner, so as to allow the calculation of several different element meshes consisting of quadelements. The following element meshes are investigated: 4,3,2,4,6 elements in the z direction x 4 elements between the x and yaxis and double the number of elements, 8,6,4,8,12 elements in the zdirection x 8 elements between the x and yaxis. The calculation is made with the program ASE. Results: Stress Stt at the outer surface of point D. Theoretical value 38.5 MPa analytically. Benchmark value 38.6 MPa. The results of the benchmark and the program ASE can be found in the following table: Mesh Benchmark ASE Point D outside Point D inside Point D outside Point D inside Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) 4,3,2,4,6 x ,6,4,8,12x Theory further results in the DATfile Input file: ic27_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 25

26 2.22 Test No IC28 Circular Paraboloid Gravity Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Selfweight In this test the shell system, depicted above, is analysed for its selfweight of p=70 kn/m³, in the zdirection, and a gravitational acceleration of 10 m/s², whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. The system is generated in such a manner, so as to allow the calculation of several different element meshes consisting of quadelements. The following element meshes are investigated: 2x2 elements, 4x4 elements and 6x6 elements. The calculation is made with the program ASE. Results: Stress Sxx at the bottom surface of point D. Theoretical value MPa analytically. Benchmark value MPa (6x6 elements). The results of the benchmark and the program ASE can be found in the following table: Mesh Benchmark ASE Point D top Point D bottom Point D top Point D bottom Sxx (MPa) Syy (MPa) Sxx (MPa) Syy (MPa) Sxx (MPa) Syy (MPa) Sxx (MPa) Syy (MPa) 2x x x further results in the DATfile Input file: ic28_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 26

27 2.23 Test No IC29 ZSection Cantilever Torsion Bending Classification: Plate, Steel Index: NAFEMS, Benchmark, Folded plates, Torsion In this test a folded plate, depicted above, is analysed for a torsional load of 1.2 MNm, which consists of two point loads, each of 0.6 MN. The analysis uses an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3. For case 1 the system is generated with an element mesh of 8x3 quadrilateral elements. In the subsequent case 2 the number of elements are doubled (16x6). The calculation is made with the program ASE. Results: Stress Sxx at point A. Theoretical value MPa analytically. Benchmark value MPa. The results of the benchmark and the program ASE can be found in the following table: s (m) ASE 16x6 elements Theory Benchmark Szz (MPa) Ssz (MPa) Szz (MPa) Ssz (MPa) Szz (MPa) Ssz (MPa) 0.0 Point A further results in the DATfile Input file: ic29_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 27

28 2.24 Test No IC30 ZSection Cantilever Beam Bending Classification: Plate, Steel Index: NAFEMS, Benchmark, folded plate, bending In this test a folded plate, depicted above, is analysed for an individual load of 6.0 MN. The analysis uses an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3. For case 1 the system is generated with an element mesh of 8x3 quadrilateral elements. In the subsequent case 2 the number of elements are doubled (16x6). The calculation is made with the program ASE. Results: Stress Sxx at point A. Theoretical value MPa analytically. Benchmark value MPa. The results of the benchmark and the program ASE can be found in the following table: s (m) ASE 16x6 elements Theory Benchmark Szz (MPa) Ssz (MPa) Szz (MPa) Ssz (MPa) Szz (MPa) Ssz (MPa) 0.0 Point A further results in the DATfile Input file: ic30_e.dat Last changed: Essential programs: ASE SOFiSTiK Verification Manual 28

29 2.25 Test No IC31 Axisymmetric Hyperbolic Shell Edge Loading Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Point load, axisymmetric state In this test a shell system, depicted above, is analysed for an axisymmetrical state, with a point load of 1 MN/radian, which is equivalent to a line load of 1000 kn/0.01m (element width=shell thickness) for a thickness of 1.0 m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 10x1 quadrilateral elements, whereby the element width is equivalent to the shell thickness of 0.01 m. In the subsequent case the number of elements are doubled for the shell axis, therefore 20x1 elements are used. The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Results: Stress Stt (Szz) in point B at the outer side of the shell. Theoretical value MPa analytically. Benchmark value MPa (20x1). The results of the benchmark and the program TALPA can be found in the following table: Mesh Benchmark TALPA Point B Point B Sxx (MPa) Szz (MPa) Sxx (MPa) Szz (MPa) (Saa) (Stt) (Saa) (Stt) 10x x Theory further results in the DATfile Input file: ic31_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 29

30 2.26 Test No IC32 Axisymmetric Hyperbolic Shell Pressure Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Linen load, axisymmetrical state In this test a shell system, depicted above, is analysed for an axisymmetrical state, with an internal pressure of 1 MPa, which is equivalent to a line load of 1000 kn/m for a thickness of 1.0 m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 10x1 quadrilateral elements, whereby the element width is equivalent to the shell thickness of 0.01 m. In the subsequent case the number of elements are doubled for the shell axis, therefore 20x1 elements are used. The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Results: Stress Sxx (Saa) in point B at the outer side of the shell. Theoretical value 50.0 MPa analytically. Benchmark value MPa (20x1). The results of the benchmark and the program TALPA can be found in the following table: Mesh Benchmark TALPA Point B Point B Sxx (MPa) Szz (MPa) Sxx (MPa) Szz (MPa) (Saa) (Stt) (Saa) (Stt) 10x x Theory further results in the DATfile Input file: ic32_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 30

31 2.27 Test No IC34 Axisymmetric Catenoidal Shell Pressure Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Line load, axisymmetricalstate : Short description In this test a shell system, depicted above, is analysed for an axisymmetrical state, with an internal pressure of 1 MPa, which is equivalent to a line load of 1000 kn/m for a thickness of 1.0 m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 10x1 quadrilateral elements, whereby the element width is equivalent to the shell thickness of 0.01 m. In the subsequent case the number of elements are doubled for the shell axis, therefore 20x1 elements are used. The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Results: Stress Sxx (Saa) in point B at the outer side of the shell. Theoretical value MPa analytically. Benchmark value MPa (20x1). The results of the benchmark and the program TALPA can be found in the following table: Mesh Benchmark TALPA Point B Point B Sxx (MPa) Szz (MPa) Sxx (MPa) Szz (MPa) (Saa) (Sbb) (Saa) (Sbb) 10x x Theory further results in the DATfile Input file: ic34_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 31

32 2.28 Test No IC37 Axisymmetric Stiffened Cylinder Pressure Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Line load, axisymmetrical state In this test a cylinder, depicted above, is analysed for an axisymmetrical state, with an internal pressure of 1 MPa, which is equivalent to a line load of 1000 kn/m for a thickness of 1.0 m. Additionally a single load of 125 kn/0.01 m, which is distributed over the cylinder thickness, is applied. For the cylinder an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 12x1 quadrilateral elements, whereby the element width is equivalent to the shell thickness of 0.01 m, and two additional quadelements on the outer side of the cylinder, for the thicker cross section, are generated. In the subsequent case 2 the number of elements are doubled for the shell axis, therefore 24x1 elements are used, with four additional quadelements on the outer side of the cylinder (for the thicker cross section). The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Results: Stress Stt at the inner side of point C. Theoretical value MPa analytically. Benchmark value 1.62 MPa. The results of the benchmark and the program TALPA can be found in the following table: Mesh Benchmark TALPA Point C inside Point C outside Point C inside Point C outside Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) 12x x Point B inside Point B outside Point B inside Point B outside 12x x further results in the DATfile Input file: ic37_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 32

33 2.29 Test No IC38 Axisymmetric Cylinder/Sphere Pressurre Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Line load, axisymmetrical state In this test a shell, depicted above, is analysed for an axisymmetrical state, with an internal pressure of 1 MPa, which is equivalent to a line load of 1000 kn/m for a thickness of 1.0 m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 1/3 are used. For case 1 the system is generated with an element mesh of quadrilateral elements, whereby the element width is equivalent to the shell thickness of m, and the width of two elements is equivalent to the cylinder thickness of m. In the subsequent case 2 the number of elements are doubled for the shell axis, therefore elements are used. The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Results: Stress Stt at the outer side of point B. Theoretical value 16.0 MPa analytically. Benchmark value MPa. The results of the benchmark and the program TALPA can be found in the following table: Mesh Benchmark TALPA Point B inside Point B outside Point B inside Point B outside Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Theory further results in the DATfile Input file: ic38_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 33

34 2.30 Test No IC39 Axisymmetric Cylinder/Sphere Pressure Classification: Shell, Steel Index: NAFEMS, Benchmark, Shell, Line load, axisymmetrical state In this test a shell system, depicted above, is analysed for an axisymmetrical state, with a line load of 1 MPa = 1000 kn/m²*1.0 m, whereby an isotropic material with an Emodulus of 210*10³ MPa and a poisson's ratio of 0.3 are used. For case 1 the system is generated with an element mesh of 4,3,2,4,6x1 elements and for case 2 with 8,6,4,8,12x1 elements, whereby the element width is equivalent to the shell thickness of m. The calculation was made with the program TALPA, because only this program can analyse an axisymmetrical state. Compare to Benchmark Test No IC27: Cylinder/Sphere Internal Pressure Results: Stress Stt at the outer side of point D. Theoretical value 38.5 MPa analytically. Benchmark value 38.6 MPa. The results of the benchmark and the program TALPA can be found in the following table: Mesh Benchmark TALPA Point D inside Point D outside Point D inside Point D outside Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) Stt (MPa) Saa (MPa) 4,3,2,4,6x ,6,4,8,12x Point C inside Point C outside Point C inside Point C outside 4,3,2,4,6x ,6,4,8,12x further results in the DATfile Input file: ic39_e.dat Last changed: Essential programs: TALPA SOFiSTiK Verification Manual 34

35 2.31 Test 5 Fundamental 2D Plasticity Benchmark Classification: 2D steel plate, plane strain conditions, elastoplastic Von Mises material a) perfectly plastic b) with isotropic linear hardening Search Terms: NAFEMS, benchmark, Von Mises plasticity, isotropic hardening, displacement control, residual stresses Short Description: Compute the stress path for a defined sequence of loading/ unloading steps for a) a perfectly plastic Von Mises material b) Von Mises material with isotropic linear hardening Detailed Description: A square steel plate of edge length L = 1 m is subjected to a sequence of eight imposed straining steps: Stretching in xdirection until the plate just yields, followed by further stretching in xdirection causing plastic flow, i.e. post yield behaviour. Stretching in ydirection in two steps. Compression in xdirection in two steps. Compression in ydirection in two steps. At the end of the final load step, the plate is returned to its original dimensions. Comparison of results see tabs below. Input File: 2Dplasticity.dat Last Changed: Mainly affected programs: TALPA SOFiSTiK Verification Manual 35

36 SOFiSTiK Verification Manual 36

37 SOFiSTiK Verification Manual 37

38 SOFiSTiK Verification Manual 38

39 2.32 Test 5 "Dynamic for Deep SimplySupported Beam" Classification: Beam, general material Search Terms: NAFEMS, Benchmark,Dynamic,Forced Vibration,Eigenvalue : Short Description Calculate the main eigenvalues of a simply supported 3D beam. Related examples: Test 5H (Harmonic Forced Vibration Response) Test 5P (Periodic Forced Vibration Response) Test 5T (Transient Forced Vibration Response) Detailed Description: The beam length is 10 m and is divided in 5 elements. The cross section is a rectangle with 2m side length. All displacements are constrained, also the torsional rotation at the beginning. Shear deformation are considered but not as a Timoshenko beam, though classic beam with shear correction factors. The matrices include rotational masses. Results: Modes DYNA NAFEMS (Closed Form Solution) NAFEMS (Exact 3D beam elem.) Flexural Modes 1 & Hz Hz Hz Torsional Mode Hz Hz Hz Extensional Mode Hz Hz Hz Flexural Modes 5 & Hz Hz Hz Torsional Mode Hz Hz Hz Flexural Modes 8 & Hz Hz Hz Input File: test5.dat Last Changed: Mainly affected programs: DYNA SOFiSTiK Verification Manual 39