shape optimization of three dimensional continuum structures via force approximation techniques the existing need to develop methods whereby the shape design efficiency can be improved through the use of high quality approximation methods is addressed an efficient approximation method for stress constraints in three dimensional shape design problems is proposed based on expanding the nodal forces in taylor series with respect to shape variations the significance of this new method is shown through elementary beam theory calculations and via numerical computations using three dimensional solid finite elements numerical examples including the classical cantilever beam structure and realistic automotive parts like the engine connecting rod are designed for optimum shape using the proposed method the numerical results obtained from these methods are compared with other published results to assess the efficiency and the convergence rate of the proposed method it is concluded that by taking advantage of this high quality approximation the total number of finite element analyses required for structural shape optimization can be reduced significantly resulting in the same level of efficiency achieved previously in sizing problems

elastoplastic truss design using a displacement based optimization abstract a displacement based optimization dbo method is applied to truss design problems with material nonlinearities to explore feasibility and verify efficiency of the method as compared to traditional structural optimization minimum weight truss sizing problems with various path independent elastoplastic laws including elastic perfectly plastic linear strain hardening and ramberg osgood models are investigated this type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the dbo setting to nonlinear problems to implement the methodology a computer program that uses the commercially available optimizer dot by vr d and imsl linear programming solver by visual numerics is developed several test problems are successfully solved using the dbo approach and solutions are compared to those available in the literature demonstrating significant reduction of computational time in comparison to the traditional structural optimization method in particular the dbo approach is found to be suitable for truss topology design since the method allows member areas to have cross sectional areas equal to zero exactly

structural optimization a new dual method using mixed variables a new and powerful mathematical programming method is described which is capable of solving a broad class of structural optimization problems the method employs mixed direct reciprocal design variables in order to get conservative first order approximations to the objective function and to the constraints by this approach the primary optimization problem is replaced with a sequence of explicit subproblems each subproblem being convex and separable it can be efficiently solved by using a dual formulation an attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs examples of application to real life aerospace structures are offered to demonstrate the power and generality of the approach presented

complexes de chaines etales et courbes de deligne lusztig abstract in a first part we lift the usual constructions of functors between derived categories of etale sheaves over schemes with a sheaf of algebras to pure derived categories for varieties with finite group actions we recover in a more functorial way rickard s construction we apply this to the case of deligne lusztig varieties and show that broue s conjecture holds for curves the additional ingredient we need is obtained from an easy property of the cohomology of etale covers of the affine line

performance analysis of optical synchronous cdma communication systems with ppm signaling direct detection optical synchronous code division multiple access cdma systems with m ary pulse position modulation ppm signaling are investigated optical orthogonal codes are used as the signature sequences of our system a union upper bound on the bit error rate is derived taking into account the effect of the background noise multiple user interference and receiver shot noise the performance characteristics are then discussed for a variety of system parameters another upper bound on the probability of error is also obtained based on chernoff inequality this bound is utilized to derive achievable expressions for both the maximum number of users that can communicate simultaneously with asymptotically zero error rate and the channel capacity our results show that under average power and bit error rate constraints there always exists a pulse position multiplicity that permit all the subscribers to communicate simultaneously

a note on decomposition numbers for groups of lie type of small rank abstract using virtual projective characters coming from the l adic cohomology of deligne lusztig varieties we determine new decomposition numbers for principal blocks of some groups of lie type of small rank including g 2 q and steinberg s triality groups d 4 3 q

partial correlation effects in direct sequence spread spectrum multiple access communication systems nearly all previous analytical results on the performance of direct sequence spread spectrum multiple access ds ssma communication systems are restricted to systems in which the period p of the signature sequence is equal to the number n of chips per data symbol in many applications however it is necessary to employ signature sequences whose period p is much larger than n thus successive n chip segments of the signature sequence are used to phase code the carrier during the transmission of successive data symbols the performance of such systems depends on the partial correlation properties of the signature sequences rather than the aperiodic correlation properties as in the case when n p in this paper we consider the performance of a ds ssma system for arbitrary values of p and n as special cases of our results we delermine the effects of partial correlation in three classes of systems those for which n p those for which n and p are relatively prime and those for which n is a divisor of p we also provide two methods for the design of sequences for systems for which n is a divisor of p

optimal material selection using branch and bound techniques a methodology for structural synthesis is presented in which the optimal material selection for the truss structures is treated in terms of 0 1 variables structural member sizes and material selection variables are treated simultaneously as design variables optimization is carried out by generating and solving a sequence of explicit approximate problems using a branch and bound strategy intermediate design variables and intermediate response quantities are used to enhance the quality of the approximate design problems numerical results for example problems are presented to illustrate the efficiency of the design procedure set forth

structural optimization using beam elements techniques for handling beam elements in structural optimization are investigated the complexities of evaluating the geometrical properties of a section stress recovery and design variable selection are successfully handled by the concept of an element library use of equivalent stress and separation of sensitivity variables and design variables program implementation is based on the use of an existing finite element analysis package and a numerical optimizer the quality of linearization of the behavior constraint functions is also investigated

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

complex reflection groups braid groups hecke algebras presentations a la coxeter are given for all irreducible nite com plex re ection groups they provide presentations for the corresponding generalized braid groups for all but six cases which allow us to generalize some of the known properties of nite coxeter groups and their associated braid groups such as the computation of the center of the braid group and the construction of deformations of the nite group algebra hecke algebras we introduce monodromy representations of the braid groups which factorize through the hecke algebras extending results of cherednik opdam kohno and others summary introduction complex re ection groups and their presentations a background from complex re ection groups b presentations braid groups and their diagrams a generalities about hyperplane complements b generalities about the braid groups c the braid diagrams proofs of the main theorems for the braid groups b de e r a notation and prerequisites b computation of b de e r and of its center for d c computation of b e e r and of its center hecke algebras a background from di erential equations and monodromy b a family of monodromy representations of the braid group c hecke algebras diagrams and tables appendix generators of the monodromy around a divisor appendix tables to mathematics subject classi cation primary g we thank jean michel peter orlik pierre vogel for useful conversations and the isaac newton institute for its hospitality while the last version of this manuscript was written up the second named author gratefully acknowledges nancial support by the fondation alexander von humboldt for his stays in paris michel brou e gunter malle raphael rouquier

performance of multiuser detection for optical cdma ii asymptotic analysis for pt i see ibid vol 43 no 11 p 2803 2811 1995 this paper presents characterizations of optimum multiuser detection in intensity modulation direct detection cdma channels based on asymptotic analysis of simple bounds on optimum performance technical difficulties in applying large deviation techniques to the evaluation of asymptotic multiuser efficiencies are rigorously addressed these same difficulties also lead to the derivation of conditions under which the linear multiuser detection achieves known interference hence optimum performance asymptotic analysis of the conventional correlation receiver including derivation of the optimal decision threshold for on off signaling formats is also presented

cohomology of deligne lusztig varieties for short length regular elements in exceptional groups abstract we determine the cohomology of deligne lusztig varieties associated with some short length regular elements for split groups of type f 4 and e n as a byproduct we obtain conjectural brauer trees for the principal 14 block of e 7 and the principal 24 block of e 8

performance analysis of direct detection optical cdma communication systems with avalanche photodiodes direct detection optical code division multiple access cdma communication systems with avalanche photodiode apd photodetectors are investigated a chernoff upper bound modified chernoff upper bound and gaussian approximation on the probability of bit error are presented for general apds and arbitrary

constructive solid geometry approach to three dimensional structuralshape optimization this paper presents a constructive solid geometry approach to generic three dimensional shape optimization the problem definition and shape control are based on constructive solid geometry whereas the assets of boundary representation are exploited to specify the physics of the problem and for meshing the object this approach is strongly coupled to an automatic mesh generator and uses to its advantage the explicit association of the finite element data with the model geometry for performing shape sensitivity analysis hybrid approximation methods are used to minimize the number of finite element analyses a classical example of a cantilevered plate with a hole and a realistic aircraft turbine disk problem are solved for optimum shape using this new approach

a modular approach for three dimensional shape optimization of structures an approach for shape optimization of three dimensional solid structures is described a major consideration in the development of this capability was the desire to use a commercially available finite element program such as nastran for analysis since nastran cannot be called a subroutine a system architecture of independently executable modules was developed in which sequential execution is controlled by job control language also sensitivities are not commonly available in commercial programs a material derivative approach was developed to obtain shape sensitivities by postprocessing finite element boundary stresses stored on files a parameterized surface description and mesh generation are provided using isoparametric mapping patches the feasible directions algorithm conmin is used for optimization several automotive related examples are used to evaluate the program s effectiveness

high quality approximation of eigenvalues in structural optimization a new function for approximating natural frequency constraints during structural optimization is presented the rayleigh quotient approximation rqa presented here icreases the quality of the approximate frequency constraint by approximating the modal strain and kinetic energies instead of the frequency eigenvalue itself

design sensitivity metric for structural dynamic response an approach to study the sensitivity of dynamic responses for structural systems with respect to a set of design parameters is presented the sensitivity is evaluated by considering the behavior of the system response when the design parameters vary within a given region of the design space the sensitivity is computed by means of approximate responses which are evaluated using approximation concepts the approximation is based on modal analysis and it is valid for general underdamped linear systems intermediate design variable and intermediate response quantity concepts are used to enhance the accuracy of the approximation in this approach modal energies and mode shapes are chosen as intermediate response quantities and they are approximated in terms of selected intermediate system parameters the approximation of these quantities requires a standard eigenvalue and eigenvector sensitivity analysis numerical results that illustrate the usefulness and effectiveness of the method are presented great insight into the behavior of the system can be gained using this methodology

three dimensional shape optimization using the boundary element method a practical design sensitivity calculation technique of displacements and stresses for three dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail then the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method the shape optimization technique suggested here is applied to determine optimum shapes of a cavity in a cube and a connecting rod

coxeter orbits and brauer trees abstract we study the cohomology with modular coefficients of deligne lusztig varieties associated to coxeter elements under some torsion free assumption on the cohomology we derive several results on the principal l block of a finite reductive group g f q when the order of q modulo l is assumed to be the coxeter number these results include the determination of the planar embedded brauer tree of the block as conjectured by hiss lubeck and malle 1995 in 25 and the derived equivalence predicted by the geometric version of broue s conjecture broue and malle 1993 7

combining global and local approximations a method based on a linear approximation to a scaling factor designated the global local approximation gla method is presented and shown capable of extending the range of usefulness of derivative based approximations to a more refined model the gla approach refines the conventional scaling factor by means of a linearly varying rather than constant scaling factor the capabilities of the method are demonstrated for a simple beam example with a crude and more refined fem model 6 refs

the brauer trees of non crystallographic groups of lie type abstract in this article we determine the brauer trees of the unipotent blocks with cyclic defect group in the groups i 2 n q h 3 q and h 4 q the degrees of the unipotent characters of these objects were given by lusztig and using the general theory of perverse equivalences we can reconstruct the brauer trees that would be consistent with deligne lusztig theory and the geometric version of broue s conjecture we construct the trees using standard arguments whenever possible and check that the brauer trees predicted by broue s conjecture are consistent with both the mathematics and philosophy of blocks with cyclic defect groups

structural optimization by multilevel decomposition a method for decomposing an optimization problem into a set of subproblems and a coordination problem that preserves coupling between the subproblems is described the decomposition is achieved by separating the structural element optimization subproblems from the assembled structural optimization problem each element optimization and optimum sensitivity analysis yields the cross sectional dimensions that minimize a cumulative measure of the element constraint violation as a function of the elemental forces and stiffness the assembled structural optimization produces the overall mass and stiffness distributions optimized for minimum total mass subject to constraints that include the cumulative measures of the element constraint violations extrapolated linearly with respect to the element forces and stiffnesses the method is introduced as a special case of a multilevel multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type numerical results are given as an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition it is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers using different computers to work concurrently on the same large problem

computationally efficient bounds for the performance of direct sequence spread spectrum multiple access communications systems in jamming environments an approach for calculating upper and lower bounds for the probability of error for asynchronous multiple access spread spectrum communication systems using deterministic codes is presented the techniques is then generalized to include multiple tone jamming the approach utilizes the cumulative distribution function of individual interference terms the computational complexity of the technique is calculated to the polynomial like results showing the multiple access performance of gold codes of lengths 31 and 127 in the presence of jamming are shown the fact that this computational technique gives upper and lower bounds is rigorously proved using the riemann stieltjes integral

bounds and construction for difference triangle sets the definition of difference triangle sets dtss and is short survey of some of their important applications is given a lower bound on the maximal element in any i j dts is then given and a construction of dtss is described finally tables of the best known lower and upper bounds on optimal dtss are presented

derived categories and deligne lusztig varieties ii this paper is a continuation and a completion of boro1 we extend the jordan decomposition of blocks we show that blocks of finite groups of lie type in non describing characteristic are morita equivalent to blocks of subgroups associated to isolated elements of the dual group the key new result is the invariance of the part of the cohomology in a given modular series of deligne lusztig varieties associated to a given levi subgroup under certain variations of parabolic subgroups we also show that the equivalence arises from a splendid rickard equivalence even in the setting of boro1 the finer homotopy equivalence was unknown as a consequence the equivalence preserves defect groups and categories of subpairs we finally determine when deligne lusztig induced representations of tori generate the derived category of representations

alternative approximation for stresses in plate structures an accurate nonlinear approximation for stresses caused by membrane and bending loads in plate structures is presented although the approximation requires only a first order sensitivity analysis it is more accurate than a simple linear taylor series expansion of the stresses with respect to the design variables or their reciprocals and is exact for statically determinate structures it requires less computation both in approximate analysis and the corresponding sensitivity analysis than other approximations with the same order of accuracy the use of this alternative approximation for plate stresses in the approximation concepts approach to structural optimization results in very rapid design convergence examples of the structural optimization of plate structures subject to stress constraints are presented to show the accuracy of this approximation

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

design space optimization using a numerical design continuation method summary a generalized optimization problem in which design space is also a design to be found is de9ned and a numerical implementation method is proposed in conventional optimization only a portion of structural parameters is designated as design variables while the remaining set of other parameters related to the design space are often taken for granted a design space is speci9ed by the number of design variables and the layout or con9guration to solve this type of design space problems a simple initial design space is selected and gradually improved while the usual design variables are being optimized to make the design space evolve into a better one one may increase the number of design variables but in this transition there are discontinuities in the objective and constraint functions accordingly the sensitivity analysis methods based on continuity will not apply to this discontinuous stage to overcome the di culties a numerical continuation scheme is proposed based on a new concept of a pivot phase design space two new categories of structural optimization problems are formulated and concrete examples shown copyright 2001 john wiley sons ltd

error probabilities for binary direct sequence spread spectrum communications with random signature sequences binary direct sequence spread spectrum multiple access communications an additive white gaussian noise channel and a coherent correlation receiver are considered an expression for the output of the receiver is obtained for the case of random signature sequences and the corresponding characteristic function is determined the expression is used to study the density function of the multiple access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error the bounds which are obtained without making a gaussian approximation are compared to results obtained using a gaussian approximation the effects of transmitter power the length of the signature sequences and the number of interfering transmitters are illustrated each transmitter is assumed to have the same power although the general approach can accommodate the case of transmitters with unequal powers

alternative approximation concepts for space frame synthesis a structural synthesis methodology for the minimum mass design of 3 dimensionall frame truss structures under multiple static loading conditions and subject to limits on displacements rotations stresses local buckling and element cross sectional dimensions is presented a variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses available options include a formulation of the nonlinear mathematcal programming problem in either reciprocal section property rsp or cross sectional dimension csd space b two alternative approximate problem structures in each design space and c three distinct assumptions about element end force variations fixed element design element linking and temporary constraint deletion features are also included the solution of each approximate problem in either its primal or dual form is obtained using conmin a feasible directions program the frame truss synthesis methodology is implemented in the compass computer program and is used to solve a variety of problems these problems were chosen so that in addition to exercising the various approximation concepts options the results could be compared with previously published work

improved transient response approximation for general damped systems a new approximation for peak transient dynamic displacements is presented this approximation is based on modal analysis and is valid for general damped structures which includes the case of actively controlled structures intermediate design variable and intermediate response quantity concepts are used to enhance the accuracy of the approximation when this high quality approximation is used within the context of the approximation concepts approach to design synthesis the overall efficiency of the process expected to be improved by reducing the number of complete analyses required for convergence numerical results that illustrate the effectiveness of the method are presented

an algorithmic approach to perverse derived equivalences broue s conjecture for ω8 2 abstract following craven and rouquier s method 8 to tackle broue s abelian defect group conjecture we present two algorithms implementing that procedure in the case of principal blocks of defect d c l c l for a prime l the first describes a stable equivalence between b 0 g and b 0 n g d and the second tries to lift such a stable equivalence to a perverse derived equivalence as an application we show that broue s conjecture holds for the principal 5 block of the simple group 8 2

performance of multiuser detection for optical cdma i error probabilities characterization of optimum multiuser performance in intensity modulation direct detection optical cdma channels is addressed analysis is based on some simple bounds on optimum performance provided by receivers with side information or by a linear decorrelating receiver numerical comparisons of the performance bounds are obtained via application of saddlepoint approximations to the multiuser photocount statistics general analytical relations comparing these approximations to similar asymptotic approximations based on the chernoff bound are also derived the numerical results illustrate the fundamental importance of two of the performance bounds in addition the numerical error probability results verify the relevance of the asymptotically based performance analysis for optical cdma in part ii

optimality conditions of the hybrid cellular automata for structural optimization the hybrid cellular automaton method has been successfully applied to topology optimization using a uniform strain energy density distribution approach in this work a new set of design rules is derived from the first order optimality conditions of a multi objective problem in this new formulation the final topology is derived to minimize both mass and strain energy in the hybrid cellular automaton algorithm local design rules based on the cellular automaton paradigm are used to efficiently drive the design to optimality in addition to the control based techniques previously introduced a new ratio technique is derived in this investigation this work also compares the performance of the control strategies and the ratio technique

load paths visualization in plane elasticity using load function method abstract the paper proposes a load function method for load path visualization and load flow calculation in plane elasticity problems the load functions are directly derived from 2d equilibrium equations the stresses are written in terms of the load functions and the load flow is calculated using the load function gradient the load functions are defined using generalized beltrami representation a constructive proof is given for the existence of load functions a set of poisson s equations in terms of load functions and stress components are developed and an efficient numerical procedure to solve them is discussed numerical results show the proposed load function method is able to define the load paths and obtain the load flow using an airy stress function for problems with available closed form solution and also can be easily integrated into the numerical approaches to calculate load paths for complex problems

reduced basis approximations of structural displacements for optimaldesign a new solution procedure for improved approximate reanalyses of structures using results of a single precise analysis is presented the proposed procedure is based on combining the computed terms of a series expansion used as high quality basis vectors with coefficients of a reduced basis expression the latter coefficients can readily be determined for each trial design by various criteria the results are measured by the errors in satisfying the analysis equations and are compared in terms of the quality of the approximations the proposed approach is suitable for various types of design variables and can be used with a general finite element model a general reanalysis procedure is introduced and the physical significance of first order approximations is demonstrated several numerical examples illustrate the effectiveness of the solution process it is shown that high quality approximations of displacements can be obtained with a small computational effort for very large changes in the design variables

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

brauer trees for blocks of cyclic defect in the groups g2 q for primes dividing q2 q 1 1 are dealt with in sl 1 where we also describe the blocks of noncyclic defect for these primes these results form part of a project proposed by walter feit namely to determine the brauer trees for all finite groups the blocks and brauer trees for the groups g 2k and g2 3k are described in s2 and a survey of all the results in this paper and in sl sz is given in s3 the conjugacy classes and character tables for

cohomological goodness and the profinite completion of bianchi groups the concept of cohomological goodness was introduced by j p serre in his book on galois cohomology 31 this property relates the cohomology groups of a group to those of its profinite completion we develop properties of goodness and establish goodness for certain important groups we prove for example that the bianchi groups i e the groups psl 2 o where o is the ring of integers in an imaginary quadratic number field are good as an application of our improved understanding of goodness we are able to show that certain natural central extensions of fuchsian groups are residually finite this result contrasts with examples of p deligne 5 who shows that the analogous central extensions of sp 4 z do not have this property

algorithm for modification of parameters in vibrating systems concluding remarks a global local approximation based on a linear approximation to a scaling factor has been presented the approximation permits us to use a global approximation based on a simple model of our problem to extend the range of usefulness of derivative based approximations to a more refined model the method was demonstrated for a simple beam example with a crude and more refined finite element model

new approximation method for stress constraints in structural synthesis a new approximation method for dealing with stress constraints in structural synthesis is presented in previous methods it has been common to create an approximation of the actual constraints with respect to the design variables and then use this with optimization to produce a new candidate design in the present method the finite element nodal forces are instead approximated and these are used to create an explicit but often nonlinear approximation to the original problem the principal motivation is to create the best approximation possible in order to reduce the number of detailed finite element analyses needed to reach the optimum the method is shown to be quite simple while providing significant efficiency gains in the overall optimization task also the method produces such high quality approximations to the original problem that the need for move limits during the approximate optimization stage is greatly reduced examples are offered and compared with published results to demonstrate the efficiency and reliability of the proposed method it is concluded that there are considerable gains yet to be achieved through continued careful investigation of approximation techniques

perverse equivalences and broueʼs conjecture abstract we give a new approach to the construction of derived equivalences between blocks of finite groups based on perverse equivalences in the setting of broue s abelian defect group conjecture we provide in particular local and global perversity data describing the principal blocks and the derived equivalences for a number of finite simple groups with sylow subgroups elementary abelian of order 9 we also examine extensions to automorphism groups in a general setting

new approximation for steady state response of general damped systems a new approximation for steady state dynamic displacements which captures the nonlinearities associated with resonance is presented this approximation is based on modal analysis and is valid for general damped structures which include the case of actively controlled structures intermediate design variable and intermediate response quantity concepts are used to enhance the accuracy of the approximations when these high quality approximations are used within the context of the approximation concepts approach the overall efficiency of the design synthesis process is improved by reducing the number of complete analyses required for convergence numerical results that illustrate the effectiveness of the method are presented

shape optimization with multiple loading conditions and mesh refinement the capability to handle multiple static loading conditions has been added to two dimensional shape optimization with adaptive mesh refinement the strain energy density variations for each mesh were normalized and then maximum values from all loading conditions were used for refinement several sample test cases were considered a two dimensional bracket with two in plane loading cases and a folded stamped sheet metal part representing an upper suspension control arm and a folded stamped sheet metal part representing a brake pedal support bracket

approximation method for configuration optimization of trusses an efficient method for truss configuration optimization is presented elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints constraints on member stresses and euler buckling are imposed and multiple loading conditions are considered the method presented here utilizes an approximate structural analysis based on first order taylor series expansions of the member forces the force approximation succeeds in reducing the degree of coupling between the sizing and geometry design variables and thereby increases the accuracy of the approximation a numerical optimizer uses information from the approximate structural analysis as it minimizes the weight of the truss

an optimization design method for large scale structures in this paper based on the mechanical property of structures a unified approximate formula with high precision suitable to several structural response functions and various types of finite elements is introduced first and then an algorithm for solving the nonlinear program is presented this algorithm is not only effective for solving the program constructed by this unified approximate formula but also easy to change the objective function and to solve the structural optimization problem with dual or multiple objective functions