Finite elements life synthesis software design for the power industry

Pergamon

00457949(94)00345-9

Compurers & Srrurrures Vol. 54, No. 3, pp. 49S497. 1995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0045-7949195 $9.50 + 0.00

FINITE ELEMENTS LIFE SYNTHESIS SOFTWARE DESIGN FOR THE POWER INDUSTRY M. Isreb Gippsland

School

of Engineering, Switchback

Faculty of Engineering, Monash University, Road, Churchill, Victoria 3842, Australia (Received

20 August

Gippsland

Campus,

1993)

Abstract-The basic power industry finite elements software design modern requirement is for the software to accommodate and integrate both optimal design for new structures and optimal remnant life design for the same structures after they have been in service or for structures already in service. This is termed life synthesis. The finite elements ‘software crisis’ as it is known in the power industry, can be defined as the lack of emerging and existing programming technologies to meet the demand of the industry for life synthesis software. In fact, there are many finite elements software design research papers for a specific structural analysis, but none on life synthesis software design. A comparison procedure of the finite elements life synthesis software design presented in this paper with available software design methodology is outlined by focusing the attention on important life synthesis aspects of a typical power industry mill casing cracking problem.

shows how the above-mentioned requirement is accommodated, integrated and optimized through common databases and algorithms. Furthermore, Fig. 1 introduces the basic concepts of finite elements life synthesis software design for power industry. Each significant block of Fig. 1 is labelled and its function is described briefly.

1. PURPOSE OF THE PAPER The

finite

elements

‘software

crisis’

as it is known

in

as the lack of the programming art to meet the demand of the industry for an integrated software approach to both optimal design for new structures and optimal remnant life design for the same structures after they have been in service or for structures already in service. Such an integrated approach is termed life synthesis. The purpose of the present paper is to present the basic concepts of finite elements life synthesis software design for the power industry. Although there are many structural analysis software design research papers in the literature, no structural life synthesis software design research paper has, to the author’s knowledge, appeared to date. the power

industry,

can

be defined

4. COMMON

Aj = BjD,>

(1)

where A, is the size (cross-sectional area or thickness) of thejth member, j?, is a prescribed constant, and D, is the vth design variable. We restrict the element moment of inertia and section moduli to the forms

Pipe finite elements are excluded from this paper. A separate life synthesis software design treatment for this type of finite element is introduced in [l]. LIFE SYNTHESIS SOFTWARE

Dl

The independent design variables employed in this paper are scalar functions of the member’s sizes and can be expressed in the form

2. SCOPE OF THE PAPER

3. STRUCTURAL

DATABASE

r, = $(Aj)

(2)

Z, = z,(A,)“,

(3)

DESIGN

and The basic power industry finite elements software design modern requirement is for the software to accommodate and integrate both optimal design for new structures and optimal remnant life design for the same structures after they have been in service or for structures already in service. This is termed life synthesis. The macrochart layout of the general life synthesis software design, shown in Fig. 1, presents a new avenue in structural optimization. Figure 1 CAS w--1

493

where n and m are positive constants. The unit moment of inertia i, depends on the physical nature of the design variable. As a consequence of (2) the element stiffness and mass matrices and the element load vector of a typical element are of the form

M. Isreb

494

NFnsuRED OPmIlrn coNDlIloNt MODEL DEFINITION (i.e.

(i.e. Deadad DroccssData

Readand

horn Strain Gaugingand Infra

Prwvrs Data)

DATABASE: DZ

DMARASE: Di

I

RvdIcwvratun Swcu

1

t

coNPuIBELDm “--STIFWRSS NnIRlcLs nnTRImS*ND aD UECUOR FOR U)(ID VECTOR LND

EpurLrDDlutt

FOmUlLRS (INIEI)

iwnrrons I 1 ‘-‘----“‘_-__‘-, I r__-“__‘--- -___..__..___...___..___..____._--...--..---I I

I

Evaluation of design.

Fig. 1. Macrochart layout of the general life synthesis optimization software design, (4) (5) and (6)

respectively, where the inertia exponent n is the same positive number associated with size-inertia relationship of the element. The unit stiffness and mass matrices [kj”], [I??‘], [mj”], [mj*)] and the vectors {gy’} and {g:“} are independent of the design variables (element size A,). The first part of eqn (4) represents the action of direct stresses, whereas the

Life synthesis

software

design

second part is due to bending or torsion. The vector {gj’)}, is the unit load vector due to size-dependent loading (gravity or thermal expansion), and {gy)} represents the effect of distributed dead loads. In the proposed synthesis, [ki’)], [k:*)], [m:‘)], [m$], [gj”)], and [gj’)] are computed and stored, in the common database Dl, separately for individual structural elements not only throughout a particular run but throughout the life of the structures at hand for the benefit of both optimal design for new structures and optimal remnant life design for the same structures, after they have been in service. This is a departure from the presently available stress analysis programs, in which only the actual matrices and vectors are stored for each finite element during a particular run. The element stiffness and mass matrices [K,] and [M,] and the load vectors {G,} are computed for each element according to eqns (4)-(6) just before assembling the structural stiffness and mass matrices [K] and [Ml, respectively as shown in Fig. 1. 5. COMMON

DATABASE

D2

(7)

where the inertia exponent n is the same positive number associated with size-inertia relationship of the element. The unit force recovery matrices [$‘)I and [sy)] are independent of element size A,. The thermal force relief vector of the element can be written as IT,) = {$}A,,

thermal force relief vectors {q} are calculated form eqns (7) and (8). The nodal force vector of each element is then computed from {&I> =

(8)

where {t,} is t le unit relief vector due to thermal expansion. The vector {t,} is independent of element size A,. The form of eqns (6) and (8) allow only for uniform temperature increase within an element, i.e. it assumes that thermal expansion causes extension without bending. This excludes the effects of thermal gradients in beams and plates, for which we would require {?I = {tj}(Aj)” and {G,} = {g,}(A,)“. Consideration of stresses follows directly. The nodal displacement vector of the structure due to the bth load condition is given by

where (ujb} is the jth element nodal displacement vector due to load condition b. In the proposed synthesis [$“I, [sj2)] and {t,} are computed and stored separately for individual structural elements into the common database D2, not only throughout a particular run but throughout the life of the structure at hand for the benefit of both optimal design for new structures and optimal remnant life design for the same structures after they have been in service. In other words, the common database D2 contains permanent storage of element design data (namely force recovery matrices, thermal stress vectors, and design information) and the design variable unit weight array.

K-‘{&~>

DESIGN ALGORITHM)

The notation AOLD in block Al is used for the current design variables, ANEW denotes the improved design and RMAX is the maximum constraint ratio. The sole objective of the uniform scaling operation of block Al is to modify the behaviour of the structure by bringing the design as close as possible to the surface of active constraints; the resulting change in weight is of minor importance. Uniform scaling operation is an efficient means of obtaining near-critical design. It is also the only available operation for large structures that will lead to a critical design other than the fully stressed design (FSD). Uniform scaling has been used extensively before in optimization programs (see [2] for example), however, its application to life synthesis is new. Uniform scaling operation can be represented by a redesign vector passing through the origin of the design space. This method of design offers two advantages over the use of standard redesign equations alone. First,

coal is mixed {Ub) =

(11)

[s,l{ujbI+ {T,),

6. BLOCK Al (OPTIMAL

As a consequence of eqn (2) the element force recovery matrix of a typical element is of the form [Sl = [.$“I + [.rj2’](A,)“,

495

for the power industry

with

(9)

where (Rb} is the load vector of the structure due to load condition 6. In practice the structure stiffness matrix is not inverted, but { Ub} is obtained by solving for the simultaneous equations

WlJU,I = l&j. Immediately after solving for the unknown ment, the element force recovery matrices

(10) displace[S,] and

Fig. 2. A sketch

of a typical

power

station

mill.

M. Isreb

496

. . . . __. . ., ~__.____..____._. Observation of Mill Casing Cracking I--

Model

Definition

1 I I I

I I

i Sta e tw (inde ndent I Solsware). The our put of I stage tw is used as an I input to stage three. I4

Model Definition Based on Neasurod operatin Conditions (i.e. Rea % and Process Data) Stage

one

(independent

Softua~)

I I I I 1 , I I I I I I 1 I I

1 I I

/.I

1

L.............................,

I

I

I

1

Stage

three

(independent

softuare).

I , I I. I I I 1 I

T’~wo&al Rnalysis

: I I I I

-;

I I L...................._, Fig. 3. Simplified flow diagram of presently available software design methodology. The sequence contents of each stage may vary slightly. However, life synthesis approach presented in this paper departure from the presently available methodology.

the use of scaling operation results in a sequence of critical designs which are very useful in monitoring the life synthesis design process. The second advantage of using scaling is that it prevents the intermediate design from departing excessively from the critical state. This in turn has a stabilising influence on the convergence of the design process. 7. REMNANT LIFE ALGORITHM A2 AND MATERIAL PROPERTIES ALGORITHM A3

Remnant life algorithm A2 calculates the calculated number of cycles to failure and corresponding reliability knowing the material properties and the stress or strain state. The algorithm A3 is the material property algorithm which is used to input new ma-

and is a

terial data using the algorithm material properties main menu if algorithm A2 is not satisfied. In other words, if the calculated number of cycles to failure and corresponding reliability in algorithm A2 is not acceptable, in this case the design is considered a new and the process starts from the beginning as shown in Fig. 1. On the other hand, if the reliability is acceptable then the remnant life algorithm A2 is satisfied and the procedure is terminated.

8. DISCUSSION

A sketch of a typical power station mill is shown in Fig. 2. The mill casing shown in Fig. 2 can be modelled as a plate with a hole (the coal mixed with

Life synthesis software design for the power industry hot furnace gas enters through this hole) and an observation window (the number of observation windows may vary from one power station to another). The finite element model of the mill casing is very similar in concept to the one shown in Fig. 1 of [3]. However, the whole model of the mill casing must be used as compared to the quarter of the model shown in [3]. This is due to lack of symmetry in regard to geometry and temperature loading of the mill casing. Cracking of the mill casing, if it occurs, usually appears in the vicinity of the openings (holes and windows). A comparison procedure of the life synthesis software design introduced in the present paper with available software design methodology is outlined by focusing the attention on important life synthesis aspects of a typical power industry mill casing cracking problem. The simple flow diagram shown in Fig. 3 gives a summary of presently available software design methodology. It should be noted that the classical analysis and design block shown in stage one of Fig. 3 can be integrated in one optimization process. Also, the sequence and contents of each stage of Fig 3 may vary slightly in concept. However, a comparison between the proposed general life synthesis optimization software design of Fig. 1 and the presently available software design

497

methodology shown in Fig. 3 reveals the advantages of the proposed software design. In addition, the proposed software design is based on life synthesis approach in accordance with optimal remnant life design path of Fig. 1. The approach is based on the integration of optimal design into life synthesis (including optimal new design path of Fig. 1). Consequently, the approach proposed in this paper yields an optimal design similar in concept to that of Fig. 2 of [3]. The synthesis software designed suggested in the present paper yields, in addition to an optimal design within the design space, the predicted number of cycles to failure and corresponding reliability based on the best available material. The measured operating conditions of Fig. 1 includes strain gauging and infra-red temperature survey. REFERENCES

1. M. Isreb, Pipe finite element life synthesis software design for petrochemical and power industry. Compur. Sfruct. 39, 431-434 (1991). 2. C. P. Rubin, Minimum weight design of complex structures subject to frequency constraint. AIAA J. 8, 923-927 (1970). 3. M. Isreb, Plate with hole under uniform end load synthesis with stress constrains. J. Structural Div., ASCE 103, 773-779 (1977).