Dr. Alexander I. Danilin Russia, Samara State Aerospace University (National Research University) METHODS OF STRUCTURAL DESIGN WITH STIFFNESS REQUIREMENTS

Dr. Alexander I. Danilin

Russia, Samara State Aerospace University (National Research

University)

METHODS OF STRUCTURAL DESIGN WITH STIFFNESS REQUIREMENTS

TASKS FOR PRACTICAL TRAINING

LEARNING THE PACKAGE DRACO (2 HOURS)

DRACO is the package for Structural Analysis and Optimization of Aerospace Structures.

It supports the training process for master’s program of aerospace engineers.

The package is developed under the personal initiative in an off-duty time by me,

© Alexander I. Danilin

and also contains realization of original algorithms for structural optimization. Inside DRACO is applied the finite element method for the analysis of structures.

The programs of the package work very fast.

Problem keeping 10965 nodes (21930 unknowns) and having a half-width of the band of the global set of equations, equal 279, from a beginning and up to the end takes for decision 18 seconds of total time on the processor 1800 MHz and hard disk Hitachi with access time 9 ms.

Dr. Alexander I. Danilin2

Module 1

LEARNING THE PACKAGE DRACO (2 HOURS) DRACO can analyse structures, finite-element model which one is within following limitations.

Quantity of unknowns - no more than 1,000,000.

Quantity of connections of one node with other - no more than 1,000.

Quantity of loadings which are simultaneously taken into account by optimization - no more than 41.

The package DRACO works under operating systems Windows® XP/Vista/7/8.

The requirements for the hardware: the RAM - 16 MB and more; a disk space ~20 MB.

The programs of the package are written in Microsoft Visual® C++ with usage the MFC® library.

All license agreements, concerned Microsoft Visual® C++ and MFC®, are completed.

DRACO - is abbreviation of DiscRete Analysis of Construction and Optimization and means the flying dragon.

All remarks and proposals You can send to e-mail: [email protected]


Module 1


The orientation of a package on problems of analysis and designing of thin-walled structures first of all aerospace type has predetermined initial library of finite elements. DRACO has the following types of elements.

1. ROD2. An element working on a tension-compression forces and intended for modelling stringers, boom of beams, rod of trusses, propping, etc.

2. MEMBRANE3 and MEMBRANE4. These elements work in the two-dimensional stress state and are intended for modelling parts of thin-walled structure by their work without buckling failure. The quadrangular element is created by modification of stiffness matrix for wall of an element BEAM4 /2/ with averaging shear stresses in wall and without taking into account correcting factors.

3. SHEAR4. It is received from MEMBRANE4 by taking into account only shear deformations. It is intended for modelling work of thin-walled structures after buckling failure.

4. BEAM4. It is a component of the [2] thin-walled beams intended for modelling working on a bending in the plane and in addition work in the two-dimensional stress state. The element serves for the description of frames, longerons and ribs.


Module 1


5. ANISOTROPIC4. An element consist membrane with two sets of rods. Each set of rods has own orientation. The element serves for modelling stiffened plates.

6. BAR2. The rectilinear rod working on a bending and shear in two planes, tension-compression and torsion.

7. PLATE3. Application of homogeneous coordinates has allowed to avoid numerical integration and increase speed of analysis.

8. SANDWITCH for modelling compartments of a wing. Element consist from two MEMBRANE4, modelling top and bottom skin of a wing, and four SHEAR4 modelling walls of longerons and ribs. The element is intended only for structural optimization of wing structures.

Elements of type 6 and 7 are intended only for structural analysis and not involved in a subsystem "Optimization".


Module 1

LEARNING THE PACKAGE DRACO (2 HOURS) Problem solving preparation

To begin job with DRACO you must run the main program

D:\Draco_21\Exec\DracoShell.exe.

The main window appears on the display:

Upper string defines pop-up menus, lower string consists information about current state of analysis.

Fac et spera (lat.) - work and hope - the field where additional information is shown by placing of cursor on some item of menu.

No Model folder select... - the field where current folder name is shown. This folder will already) consists FEM-model.

No Task select... - the field where selected function is shown.

User must choose the function for execution. This is made in menu What to do?


Module 1


DRACO suggests the following facility:

Structural Analysis - stress and displacement definition by different loadings and boundings.

Structural Optimization – material distribution only with taking into account strength requirements in several loadings and boundings.

Structural Optimization with Displacement Constraints - material distribution with taking into account strength requirements in several loadings and boundings and displacement constraints.


Module 1


Structural Optimization with Strong Displacement Constraints - material distribution with taking into account strength requirements in several loadings and boundings and displacement constraints as strong equalities.

Modal Analysis – calculation of the natural frequencies and modes.

Dynamic Properties Optimization - material distribution with taking into account strength requirements in several loadings and boundings and constraints on natural frequencies of structure.

New Optimization Theory – research part of DRACO – searching NOT fully stressed structure with minimal own mass.


Module 1


After function selection you have to define Model Placing.

You enter in pop-up menu and after all manipulation you have to achieve, as example, the following window.


Module 1

LEARNING THE PACKAGE DRACO (2 HOURS) Create and check a model. All pop-up menu you find in “Pre-Processor” item.

ATTENTION

DRACO does NOT carry out any conversions of physical values. Physical data consistency is on your own responsibility.

Name of the file with model information must be “model.txt”.

Which model is there, is defined by the folder in which that file is saved.

Direct input of a finite element model allows to use all type of the finite elements of DRACO.

However, analyst must know both files structure of DRACO and information structure for each file of model. Read, please, the chapter Information Structure.

The first, analyst must prepare by hand all information about finite-element model. After that, he can input these data. Input is carried out with help any text editor in “txt” format in code page ®Windows 1252.

We show here the example of file “model.txt” for the beam from 29 elements “Beam”, fixed and loaded as shown here.


Module 1


The information about model is prepared as the tables and input by columns.

<Commands explanation>

<...> < Comment, can be input in any place >

ddd ddd ... ddd; = SIMPLE GROUP, ddd – decimal digits, number from number separated by space

ddd s ddd r ddd; = CYCLE GROUP: number ddd repeat ddd times with the step ddd

s = STEP, if absent, then s = 0

r = REPEAT

; = GROUP END GROUP NESTING is forbidden!!!

@ = COLUMN END

{ ... } = BEGIN and END of information block

Type of information (key words).

Nodes (Nodes coordinate in Cartesian system),

Types of Element

Rod2, Beam4, Membrane3, Membrane4, Shear4, Anisotropic4, Sandwich.

More input information.

Materials (Materials performances), Loading (Actual loading for each case), Bounding (Actual bounding for each case), Analysis (# Loading and #Bounding), Optimization (Conditions of Optimization), UnitLoad (For optimization with displacement restriction), Masses (Lumped mass values), Frequency (Required frequencies values for dynamic optimization)Dr. Alexander I. Danilin

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Module 1


<========= Beam Model ===============================>

Nodes <Nodes number> 60;

{ <Nodes coordinate>

<X> 0s100r30; 0s100r30; @

<Y> 200r30; 0r30; @

<Z> 0r60; @ }

<------------------------------------------------------------------------------------>

Beam4 <Elements number> 29;

{ < # Element> 1s1r29; @

< # Material > 1r29; <For I-cap i-j > @

1r29; < For I-cap k-l > @

1r29; < For wall > @

<Topology> 1s1r29; <First column, node i > @

2s1r29; <Second column, node j > @

32s1r29; <Third column, node k > @

31s1r29; < Fourth column, node l > @

<Stiffness> 100r29; <Cross-area of I-cap between nodes i-j> @

100r29; < Cross-area of I-cap between nodes k-l> @

1r29; <Wall thickness> @

<I-cap eccentricities > <Between nodes i-j> 0r29; @

< Between nodes k-l> 0r29; @ }Dr. Alexander I. Danilin12

Module 1


<------------------------------------------------------------------------------------------------------------------------------------->

Masses < # Mass case> 1

<Mass quantity> 1;

{

<# node> 30; @

<Mass value> 500; @

}

<------------------------------------------------------------------------------------------------>

Loading < # Loading> 1 <Forces quantity> 2;

{

302 602; < Force direction code>

<Force direction = (# Node) * 10 + DIR; DIR = 1 along X-axis, 2 along Y-axis, 3 along Z-axis > @

1000 1000; <Force values> @

}

<------------------------------------------------------------------------------------------------------------------------------------->

Bounding < # Bounding> 1 < Fixed displacement quantity> 4;

{

11 12 311 312; < Displacement direction code – see Force direction code > @

0r4; <Displacement value> @

}Dr. Alexander I. Danilin

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Module 1


<------------------------------------------------------------------------------------------------------------------------------------->

Analysis

{

1 0; < # Bounding> @

1 0; < # Loading > @

< ZERO at the end is necessary; it is the end-flag in corresponded file in DRACO package>

}

<------------------------------------------------------------------------------------------------------------------------------------->

Optimization

{

1000; @ < Initial mass value. Is used only in “Optimization by new theory”>

< Technological restriction on thicknesses in percent from it’s initial values>

0; @ <Minimum. If set 0, then restriction is absent>

0; @ <Maximum. If set 0, then restriction is absent >

1 0; @ < # Bounding >

1 0; @ < # Loading>

0.4 0; @ < Given value of displacement, which defined by unit loading>

100 0; @ < Scale of Unit loading>

0; @ 0; @ < Reserve >

0; @ 0; @ < Reserve >

}Dr. Alexander I. Danilin

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Module 1


<------------------------------------------------------------------------------------------------------------------------------------->

Materials

{ 1s1r16; < # Material >@

72000; 0r15; <Modulus of elasticity> @ <ZERO – end mark>

0.3333; 0r15; @ < Poisson ratio >

1000; 0r15; @ < Allowable strength>

0r16; @ 0r16; @ 0r16; @ 2780;

0r15; @ < Density >

0r16; @ 0r16; @ 0r16; @ 0r16; @ 0r16; @ 0r16; @ 0r16; @ 0r16; @ }

<------------------------------------------------------------------------------------------------------------------------------------->

Frequency < Only for natural vibration analysis>

{ 1 0; @ < # Bounding> < ZERO – end mark>

1 0; @ < # Mass case > }

<========== End of Beam Model Input Information ==============>

It possible to create and edit that text file from DRACO. For this you have to enter in menu “Create” and “Direct input the FE-model”. Before you have to define the folder for model, and then “Create file” and “Edit Model”. DRACO uses R-WIN® Editor version 5.02 from "Proxima Software" distributed free in internet. Dr. Alexander I. Danilin

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Module 1

LEARNING THE PACKAGE DRACO (2 HOURS) To check information about the model. All pop-up menu you find in “Pre-Processor” item.

Model drawing is necessary for verification of input model.

On the following image you see two kind of model presentation: with and without elements separation. Mistakes are visible.


Module 1

STRUCTURAL OPTIMIZATION (8 HOURS)We suggest the set of problems, which show the path of external forces optimal transition. Some of them are shown here.

Problem 1.

The square plate is fixed on the left edge and the force is applied in right upper angle. The line of act of this force goes into the left lower corner of plate, as is shown in drawing.

The shortest path will lead to "create" additional forces.Dr. Alexander I. Danilin17

Module 1

STRUCTURAL OPTIMIZATION (8 HOURS)Problem 1.

The force goes directly on the bearing.


Module 1


Now we will create on a path of force an obstruction. We will excise at plate center a square hole...


Module 1


Optimal structure


Module 1

STRUCTURAL OPTIMIZATION (8 HOURS)Problem 2. We suggest not only plane structures for optimization. Next go example of wing.

Model Stress in skin

Skin optimal thickness Force path in skinDr. Alexander I. Danilin21

Module 1

STRUCTURAL OPTIMIZATION OF FORWARD SWEPT WINGS (8 HOURS)

As an example of application optimization method we suggest to design the forward swept wing structure with constraint on twist angle of the wing section placed on Z = 0.81.

We choose the constraint to exclude the divergence in flight.

As prototype we consider the wing with the form in plane from airplane Sukhoi S-47 “Berkut” but having another sizes and made from isotropic material.


Module 2


As initial material distribution we take the identical thickness for skin and wall of ribs. Wall of spars have the thickness 2.5 times more. Caps of spars and ribs are also identical. We have set the stiffness of structure superfluous, because we would like to show that absolute values of stiffness is NOT guarantee of the conceptual absence of divergence. Wing Y-deformation with the initial distribution of material is shown here.


Module 2


After optimization with using the developed theory we have achieved the Y-displacements, shown on the next picture. It can be seen that elastic twist angles of the aerofoil placed on Z = 0.81 are negative along the wing.

Therefore the divergence of such wing is impossible.


Module 2


We suggest to optimize several new wing configurations, for instance such as the following.

The new type of combined wings are

represented on these pictures.

These aircrafts have high cruise speed

(low local shock wave drug due swept

parts of wing) and good takeoff and

Landing characteristics (due forward

swept and unswept parts).


Module 2

Dr. Alexander I. Danilin 26Module 3

STRUCTURAL OPTIMIZATION WITHT VIBRATION REQUIREMENTS (8 HOURS)

As the example, let's consider hypothetical swept wing to which the engine is attached on a pylon as is shown on Fig. 1.

The wing has a span 10m, aspect ratio λ = 4.38, wing taper ratio η = 2.24.

The engine is disposed on distance z=2490мм from an airplane axis.. Sweepback angle at the leading edge is χ=280, along front spar χ = 250.

With the unit load on a wing equal p0 = 450 dN/m2 aircraft all-up mass is m0=10280kg.

With thrust-to-weight ratio = 0.31 the engine thrust is 1600dN and its mass is meng=320kg (the specific mass of the engine is 0.2).

Fig. 1



With such initial data the structural optimization gives volume of full-strength design for half wing Vstrength = 0.0509m3, that with the material density ρ=2780kg/m3 leads to a mass of a structural material mstrength=142kg.

The volume of a material of the pylon and the engine nacelle are included in this volume and, accordingly, in mass. Material distribution is shown on Fig. 2

We take this material distribution as an initial allocation and compute natural modes and frequencies, which are presented on the next slide.

Fig. 2



Table 1. Natural frequencies of the full-strength structure.

Value of passive masses is 797kg and includes mass of non-structural elements of the wing, mass of the pylon and the engine nacelle, and also mass of the engine. Thus, the total mass of model presented on Fig. 2 is 939kg; from this mass the share of the structural material, responsible for creation of rigidity is equal 15%. Fig. 3

Number of frequency

Value [1/s] Form

ω1 1.559 Bending

ω2 1.939 Torsional

ω3 2.203 Bending-torsional






Let's conduct optimization of allocation of a material with the simultaneous taking into account the strength requirements and dynamic stiffness.

As the limitations of natural frequencies we will take the following values: ω10 = 2.027 1/s (magnification on 30%); ω20 = 2.908 1/s (magnification on 50%).

We will vary thickness of skin of a pylon and a wing, a spars and ribs cap, and also walls of spars. New values of skin thickness we will assign as maximum from the bending and twisting moments in appropriate section, caps of spars - only from bending, and walls of spars - only from torsion moment.

The suggested algorithm has converged with an exactitude of 5% after 5 iterations. The repetitive process course is represented in Table 2. The discovered material distribution is displayed on the next slide.

Table 2. Iterative process course.Freq# Initial 1 iter. 2 iter. 3 iter. 4 iter. 5 iter.

ω1 1.559 2.118 1.906 2.041 1.865 2.039

ω2 1.939 3.202 2.510 3.009 2.461 2.924

ω3 2.203 4.415 2.942 4.503 2.885 4.431

ω4 4.501 6.791 5.976 6.258 5.997 6.294

ω5 5.457 8.051 7.159 7.013 7.641 7.272

ω6 6.154 10.883 8.950 10.158 8.835 10.113

V [m3] 0.0509 0.0956 0.0748 0.0867 0.0782 0.0821

m% 15 25 20.7 23.2 21.4 22.2





We show that with using developed methods the additional material is placed in areas where it works effectively: for simultaneous magnification of the first natural frequency on 30% and second natural frequency on 50%, relative mass of structural material increased only on 7.2%.

• ______________________________________________________________________________

• INFORMATION

• Samara State Aerospace University (National Research University) begins the project for research the problems concerned hypersonic airliner development.

• We have new ideas (and funding) for development in different areas of hypersonic aircraft engineering.

• We invite all researchers, especially young scientists and engineers to join us in our investigations.

• Contact: Prof. Danilin A.I., e-mail: [email protected]

Documents

Dr. Alexander I. Danilin Russia, Samara State Aerospace University (National Research University) METHODS OF STRUCTURAL DESIGN WITH STIFFNESS REQUIREMENTS