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This manual presents solved verification models including NAFEMS problems.
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This manual presents solved aerospace verification models including NAFEMS problems.
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OS-V: 0720 Straight Cantilever Beam
MacNeal-Harder Test This is a straight cantilever beam solved with solid and shell elements. Three models (rectangular, parallelogram, trapezoidal) are made with each element's type to investigate the effect of distorted elements with a high aspect ratio.

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Verification Problems
This manual presents solved verification models including NAFEMS problems.
- Aerospace Verification
  This manual presents solved aerospace verification models including NAFEMS problems.
  - NAFEMS Linear Elastic
  - Elements
    - OS-V: 0700 Twisted Cantilever Beam (Implicit Results)
      MacNeal-Harder Test This is a twisted cantilever beam solved with solid and shell elements. A model is made with each element's type to investigate the effect of distorted elements with a high aspect ratio.
    - OS-V: 0710 Curved Cantilever Beam
      MacNeal-Harder Test This is a curved cantilever beam solved with solid and shell elements. A model is made with each element's type to investigate the effect of distorted elements with a high aspect ratio.
    - OS-V: 0720 Straight Cantilever Beam
      MacNeal-Harder Test This is a straight cantilever beam solved with solid and shell elements. Three models (rectangular, parallelogram, trapezoidal) are made with each element's type to investigate the effect of distorted elements with a high aspect ratio.
    - OS-V: 0730 Scordelis-Lo Roof
      MacNeal-Harder Test The Scordelis-Lo Roof is a classical benchmark problem for shell elements. Analytical and experimental investigations were initially performed by Scordelis and Lo.
    - OS-V: 0740 Curved Strip Hook
      Raasch ChallengeThe Raasch challenge is a curved strip hook problem with a tip in-plane shear load, posed in 1990 by Ingo Raasch of BMW in Germany. The problem poses a significant challenge to shell elements because of the inherent coupling between three modes of deformation: bending, extension, and twist. OptiStruct is benchmarked against the Raasch challenge to assure its shell elements performance on Linear Static Analysis.
    - OS-V: 0750 Radial Stretching of a Cylinder
      Illustrates the use of asymmetrical elements (CTAXI) under uniform radial displacement in OptiStruct.
    - OS-V: 0760 MacNeal-Harder Solid Patch Test
      MacNeal-Harder TestThe patch test is a classical benchmark problem for the element. If it produces correct results for the test, the result for any problem solved with the element will converge toward the correct solution. The intended purpose of the proposed problem set is to ascertain the accuracy of finite element in various applications.
  - Aeroelastic Analysis
- NAFEMS Linear Elastic
- NAFEMS Thermo-elastic
- NAFEMS Heat Transfer
- NAFEMS Nonlinear Static Analysis
- NAFEMS Dynamic Response Analysis
- NAFEMS Random Response Analysis
- NAFEMS Normal Modes Analysis
- NAFEMS Composites
- Response Spectrum Analysis
- Elements
- Materials
- Fatigue Analysis
- Rotor Dynamics
- Frequency Response Analysis
- Explicit Dynamic Analysis
- Aeroelastic Analysis
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OS-V: 0720 Straight Cantilever Beam

MacNeal-Harder Test This is a straight cantilever beam solved with solid and shell elements. Three models (rectangular, parallelogram, trapezoidal) are made with each element's type to investigate the effect of distorted elements with a high aspect ratio.

veri_straight — Figure 1. FE Model of the Beam with Boundary Conditions and Loadcases

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

Six types of elements are used for this problem. They are tria-shell, quad-shell, and hexa-solid elements, each with 1st and 2nd order. Four loading cases, extension, in-plane bending, transverse bending, and twist, are used for each model. For the extension and bending load cases, unit loads are applied in a consistent fashion over all of the nodes at the tip of the beam. For the twist load cases, a unit moment is applied at the tip.

Theoretical solutions for the deflections at the tip, computed by beam theory, are:


Load Type	Component	Value
Extension	UX	0.00003
In-plane bending	UZ	0.1081
Transverse bending	UY	0.4321
Twist	ROTX	0.03208

Linear Static Analysis Results

All results are normalized with the target value.

Table 1. (a) Rectangular
	In-plane Extension	In-plane Bending	Transverse Bending	Twist
QUAD4	1.000	0.992	0.981	0.941
QUAD8	1.006	1.000	1.016	0.953
TRI3	1.000	0.032	0.973	1.072
TRI6	1.006	0.994	1.001	0.950
HEX8	0.988	0.978	0.973	0.892
HEX20	1.008	0.992	0.992	0.905

Table 2. (b) Parallelogram
	In-plane Extension	In-plane Bending	Transverse Bending	Twist
QUAD4	1.000	0.712	0.981	0.905
QUAD8	1.008	0.999	1.015	0.937
TRI3	1.000	0.012	0.955	0.931
TRI6	1.005	0.962	0.995	0.982
HEX8	1.012	0.624	0.529	0.820
HEX20	1.008	0.976	0.977	0.905

Table 3. (c) Trapezoidal
	In-plane Extension	In-plane Bending	Transverse Bending	Twist
QUAD4	1.000	0.173	0.964	0.869
QUAD8	1.005	0.981	1.015	0.950
TRI3	1.000	0.019	0.965	1.175
TRI6	1.006	0.972	0.999	0.947
HEX8	1.010	0.047	0.030	0.563
HEX20	1.008	0.902	0.950	0.905

Reference

MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1 (1985) 3-20.