Planar Truss Structure Research Articles

A REFINED STRUT-TIE MODEL APPROACH AND ITS APPLICATION TOOL.

This paper presents a refined strut–tie model approach and its application tool for the analysis and design of structural concrete. In this approach, non-linear techniques are incorporated in the development, analysis and verification processes of a strut–tie model. The additional positioning of concrete ties and steel struts at the locations of steel ties and concrete struts, respectively, is also incorporated. The proposed approach can eliminate the limitations the current strut–tie model approach has in the prediction of the behaviour and strength of structural concrete as well as in the precise design of structural concrete which experiences non-linear behaviour. The interactive computer graphics programme for the refined strut–tie model approach consists of three parts. The first and second parts are considered as the pre- and post-processors for a finite-element analysis of two-dimensional plain concrete and plane truss structures. The third part is a design routine for dimensioning and detailing the components of the developed strut–tie model. The use of the interactive computer graphics programme in the refined strut–tie model approach is illustrated with an example of the analysis of a reinforced concrete deep beam tested to failure. The refined strut–tie model approach with computer graphics capabilities can provide effective and consistent solutions to a large number of complex analysis and design problems.

A refined strut–tie model approach and its application tool

This paper presents a refined strut–tie model approach and its application tool for the analysis and design of structural concrete. In this approach, non-linear techniques are incorporated in the development, analysis and verification processes of a strut–tie model. The additional positioning of concrete ties and steel struts at the locations of steel ties and concrete struts, respectively, is also incorporated. The proposed approach can eliminate the limitations the current strut–tie model approach has in the prediction of the behaviour and strength of structural concrete as well as in the precise design of structural concrete which experiences non-linear behaviour. The interactive computer graphics programme for the refined strut–tie model approach consists of three parts. The first and second parts are considered as the pre- and post-processors for a finite-element analysis of two-dimensional plain concrete and plane truss structures. The third part is a design routine for dimensioning and detailing the components of the developed strut–tie model. The use of the interactive computer graphics programme in the refined strut–tie model approach is illustrated with an example of the analysis of a reinforced concrete deep beam tested to failure. The refined strut–tie model approach with computer graphics capabilities can provide effective and consistent solutions to a large number of complex analysis and design problems.

Hybrid expert system for qualitative and quantitative analysis of truss structures

The so-called hybrid expert systems for the analysis of physical systems (e.g. mechanical ones) integrate modelling and simulation methods, including classical numerical( quantitative) methods as well as recently developed qualitative analysis methods, using the expert-system rule-based techniques. The diagrammatic representation methods also turn out to be important elements of the knowledge representation (especially the qualitative knowledge) and user interface in such systems. In this paper, problems in the construction of such systems are discussed, using an example of an experimental hybrid system for the analysis of planar truss structures (currently in the final stages of implementation).

Damage Identification of Truss Structures Based on Vibratory Data.

The present paper shows a damage identification method of truss structures using a flexibility matrix which can be constructed from several low degrees of natural vibration frequencies and modes. The damage location in truss structures is detected from the change of the axial strain component in each truss member under virtual load before and after damage. The present method is verified through numerical examples of plane truss structures. We examine the effect of several factors on the identification of damage location, i.e., the effect of the number of vibration modes, the number of measurement degrees of freedom and measurement errors.

Reduced-Dimensionality Geometric Approach to Fault Identification in Stochastic Structural Systems

An information-based reduced-dimensionality formulation of the recently introduced geometric approach to fault identification in stochastic structural systems is presented. The feature vector, which conveys the system information used in fault identification and is a key element of the general geometric approach, is transformed into a suitable coordinate system, within which information compression may be best achieved. Dimensionality selection is subsequently based on bounding of the information loss, expressed in terms of logarithmic entropy, below a certain threshold. The information-based reduced-dimensionality formulation thus presents a formal and systematic procedure for the proper selection of a minimal dimensionality feature vector and leads to substantial simplification and potentially improved fault identification. Its application to fault identification in a laboratory-scale beam and a planar truss structure demonstrates high effectiveness and performance characteristics essentially equivalent to those of the full-dimensionality formulation.

Improved First-Order Approximation of Eigenvalues and Eigenvectors

A method based on reduced basis approximation concepts is presented for improved first-order approximation of eigenvalues and eigenvectors of modified structural dynamic systems. The terms of a local approximation based on Taylor or matrix power series are used as basis vectors for approximating the perturbed eigenparameters. For each eigenmode, a reduced eigensystem is generated by using the baseline eigenvector and the first-order approximation term as Ritz vectors. The solution of the reduced eigensystem leads to two possible estimates of each perturbed eigenvalue and eigenvector. Criteria for selection of the best approximation are presented. The zero- and first-order Rayleigh quotient approximation can be directly recovered as special cases of the present method. Results are presented for approximate dynamic reanalysis of a 25-bar planar truss structure. It is shown that high-quality approximation of the perturbed eigenparameters can be obtained for moderate perturbations in the stiffness and mass matrices. For very large local perturbations of the structure, including deletion of some structural members, it is shown that the present method yields reasonable-quality approximations.

Structural Damage Assessment with Combined Data of Static and Modal Tests

The purpose of the present study is to propose an improved damage detection and assessment algorithm based on the method of system identification. In this approach, the complete sets of modes or displacements are not needed since the error function involves only the differences between components of those vectors. The present approach allows the use of composite data, which consist of static displacements and eigenmodes. In the dynamic test, the curvature and slope of mode shapes are introduced to formulate the error responses. Using these techniques, a parametric study is conducted and the effectiveness of the method is discussed. Generally, the developed algorithm is also able to detect and assess damages in a structure when the measured data are sparse. To examine the capability of the proposed damage assessment algorithm, a series of tests for a predetermined damaged two-span continuous beam and a planar bowstring truss structure are performed. The comparisons of proposed theory with test data show good agreement. The most clear effect of the algorithm is that the combination of the curvature or slope of mode shape and the static displacement data gives the most promising results for damage detection and assessment. The proposed method can be effectively used to detect and assess possible damage in a structure.

A Response Surface for Structural Optimization

Abstract Structural optimization is computationally intensive. Typically, a finite element model must be solved repeatedly during the process. Accordingly, various approximation schemes have been developed to reduce the cost of solves or to eliminate solves entirely during portions of the optimization process. In this paper, a new type of approximation or interpolation function in the form of a global response surface is described. With this function, approximations can be made with a limited amount of calibrating data points. The response surface requires no matrix inversions for coefficient evaluation, and therefore it is relatively efficient and stable. The new response surface is used in conjunction with a modified zero-order Powell search algorithm. The effectiveness of the response surface is evaluated for a reasonably realistic offshore structure application. This planar truss structure is subjected to a deck load, a lateral wave load (considered quasi-static), and member self-weight loads. The objective for this test case was to minimize the structural cost. Nodal coordinates were considered to be the explicit design variables. Response surface results are compared with those obtained by the common optimization algorithms: steepest descent, conjugate directions, and a conventional implementation of Powell’s method. The response surface appears to be effective for the test case considered.

Damage Detection and Assessment of Structures from Static Response

A damage detection and assessment algorithm is developed based on a parameter estimation with an adaptive parameter grouping scheme. Damage is characterized by a reduction in a constitutive property of a parameterized finite-element model between two time-separated inferences. We assume that the baseline parameter values are known. An adaptive parameter grouping scheme is proposed to localize damage in a structural system for which the measured data are sparse. A data perturbation scheme is proposed both for the baseline structure, to establish the damage threshold above which damage can be confidently discerned from noise, and for the damaged structure, to compute the damage indices. To examine and illustrate the damage assessment algorithm, a numerical simulation study on a planar bowstring truss structure is performed.

Geometric Approach to Nondestructive Identification of Faults in Stochastic Structural Systems

A novel geometric approach to the nondestructive identification of faults in stochastic structural systems, based on vibration test data, is introduced. The approach uses a partial and reduced-order dynamic system model, a properly selected stochastic feature space, the notion of fault mode as the union of all faults of one particular cause, and its approximate geometric representation as a subspace of the feature space. Fault identification is accomplished by determining the fault mode subspace within which the current fault lies. The geometric approach offers important advantages over alternative structural fault identification schemes, including its inherent accommodation of stochastic effects, the use of a minimal number of measurement locations, and its ability to operate on any type of vibration data and use only partial and reduced-order models, while relaxing the need for stiffness matrix or modal parameter estimates. Its effectiveness is demonstrated via fault identification in a laboratory-scale beam and a finite element model of a planar truss structure, where the importance of stochastic effect accommodation is addressed.

Parallel processing in optimal structural design using simulated annealing

The need to reliably solve large structural design optimization problems in a reasonable time frame naturally leads to the investigation of the scope of parallel processing in optimization. Parallel optimization may be approached in two general ways. First, the analysis could be the target of parallel processing specially if it is significantly large compared with the overall computation. The second approach is the parallel implementation of the optimization algorithm, which can then be easily adapted for solving any appropriately formulated optimization problem. In this work the basics of parallel computer architectures and some popular parallelization strategies are described. Simulated annealing (SA), a stochastic, discrete optimization technique, is chosen for its global capability, robustness, and suitability for parallel processing. The concept of in SA, which simulates re-annealing, is introduced. The beneficial effects of shakeup for escaping local optima is demonstrated by solving a two-dimensional multimodal optimization problem. A pin-jointed 10-storied multibay plane truss structure is considered as an example optimization problem and has been solved using both serial as well as parallel versions of the S A algorithm. The parallel result, achieved with a relatively small parallel configuration of the computer, indicates that very large structural designs can be optimized in much shorter times along with high probability of achieving global solutions even on moderately sized parallel computers.

Structural damage detection using constrained eigenstructure assignment

System health monitoring of aerospace vehicles is important not only for conducting safe operation but also for maintaining system performance. Structural health along with sensor and actuator malfunction must be monitored to perform the system health monitoring. As a step toward developing a system health monitoring scheme, this paper investigates structural damage detection using a constrained eigenstructure assignment. The eigenstructure assignment is selected for the investigation since it may be used not only to perform structural damage detection but also to monitor the sensor and actuator performance in a unified manner. To employ the eigenstructure assignment in the framework of structural modeling and modal testing, a concept of constrained eigenstructure assignment is developed. The constrained eigenstructure assignment makes it possible that the computed feedback gains correspond directly to the structural parameter changes. To demonstrate the capability of the approach, a 20-bay planar truss structure is employed. Modal tests are performed using 11 accelerometers for the undamaged structure and several missing member damage cases. Then the test modes are used to locate the missing member. In spite of incomplete mode shapes and test inaccuracies, accurate damage detection is conducted.

Improved Inverse Eigensensitivity Method for Structural Analytical Model Updating

In order to update analytical models of practical engineering structures, inverse eigensensitivity method (IEM) has been developed. Though it has nowadays been widely accepted, the classical inverse eigensensitivity method does have some drawbacks such as the assumption of small error magnitudes and slow speed of convergence due to the fact that the sensitivity coefficients are calculated purely based on modal data of analytical model. In the present paper, an improved inverse eigensensitivity method, which avoids the existing problems of classical inverse eigensensitivity method, has been developed. The improved method employs both analytical and experimental modal data to calculate the required eigensensitivity coefficients which are very close to their true values. The method has been further extended to the case where measured coordinates are incomplete. Practical applicability of the method has been assessed by its application to the updating of the finite element model of a plane truss structure.

Homology Design for Quadratic Curves under Stiffness Constraint.

A new formulation for homology design is proposed based on the finite element sensitivity analysis. The constraint for homology design is neatly represented by a vector equation with respect to nodal displacements. Homology design to maintain a quadratic curve in a structure before and after the deformation can be efficiently carried out due to the straightforward representation of the constraint. An inequality constraint to maintain structural stiffness is added to the homology design. The inequality constraint is transformed into the equality constraint by introducing slack variables. The governing equation of the design variables is derived by the combination of these two equality constraints and solved by means of the Moore-Penrose generalized inverse. The first-order sensitivity analysis is utilized in the derivation. The validity of the proposed method is demonstrated in the numerical examples using a planar truss structure. Quadratic curves, such as the parabola and circular arc, are formed for the structure by assigning design variables to cross-sectional areas of the members. The limitation of nodal displacement is imposed as an inequality constraint to maintain the stiffness of the structure.

Automatic Truss Design by Optimized Growth

A new algorithm for the automatic design of planar truss structures is described. The designer need only specify the location of the supports, and the location and magnitude of the loads. The algorithm allows the computer to automatically synthesize a practical topology for a structure based on these specifications. The technique mimics the natural process of evolution where complex organisms evolve from successful less-sophisticated organisms. Using the proposed synthesis technique, structures are made to grow from a simple generic shape to complex forms along an optimized pathway. As the structure grows, new members are added in an organized fashion. The technique could provide two main benefits. The cost of designing structures could be reduced, and the computer could produce innovative structural topologies that a designer might not consider. The technique is illustrated by presenting the results of synthesizing a design for a high-voltage cable-support tower and by comparing results with a prominent topology optimization technique.

Design of a fuzzy controller for trajectory tracking of adaptive truss structures

A three-step design procedure for a fuzzy controller for the trajectory-tracking problem of adaptive truss structures is presented. The generation of the fuzzy rules is based on the inverse kinematics equations of the structure. The proposed procedure provides a systematic way of designing a fuzzy controller and greatly reduces the computation burden. The general guidelines for determining design parameters are also addressed. The procedure is demonstrated on a planar truss structure and the results are satisfactory and effective.

Neural network approximations in a simulated annealing based optimal structural design

The present paper examines the feasibility of using neural network based function approximations in conjunction with a simulated annealing (SA) strategy for optimization of structural systems. Such a stochastic search method is more “tolerant” of errors in objective and constraint function information than the more traditional mathematical programming techniques. The improved counterpropagation (CP) neural network is used to generate these approximations, and includes features such as dynamic adjustment of the network size, optimization based training of outstar weights, andfuzzification of output. The CP network is easy to train, and preliminary numerical results indicate that the modifications to the network significantly improve the quality of function approximations. The SA based search for optimal designs is illustrated by the sizing of planar and spatial truss structures for minimum weight and constraints on allowable stress levels.

Sensitivity based method for structural dynamic model improvement

Sensitivity analysis, the study of how a structure's dynamic characteristics change with design variables, has been used to predict structural modification effects in design for many decades. In this paper, methods for calculating the eigensensitivity, frequency response function sensitivity and its modified new formulation are presented. The implementation of these sensitivity analyses to the practice of finite element model improvement using vibration test data, which is one of the major applications of experimental modal testing, is discussed. Since it is very difficult in practice to measure all the coordinates which are specified in the finite element model, sensitivity based methods become essential and are, in fact, the only appropriate methods of tackling the problem of finite element model improvement. Comparisons of these methods are made in terms of the amount of measured data required, the speed of convergence and the magnitudes of modelling errors. Also, it is identified that the inverse iteration technique can be effectively used to minimize the computational costs involved. The finite element model of a plane truss structure is used in numerical case studies to demonstrate the effectiveness of the applications of these sensitivity based methods to practical engineering structures.

Knowledge‐based Expert systme for Judgement of Structural Stablity by Foam Feature Analysis

Abstract: This paper presents an elementary approach to artificial intelligence in structural engineering with the aid of the scheme of geometric modeling in computeraided design. In order to generate a specific form feature the structural shape information is explicitly represented, using a frame language developed in Prolog. Thus, reasoning stableness of structures in this system are interpreted as a sequential instantiation of a frame structure in which attributes stand for topological data and procedural knowledge, and as a candidate generation of a substructure of the stable form. Illustrative examples for a plane truss structure are described. Also, some comments on its applicability to an intelligent tutoring system for structural analysis and architectural design are provided, with reference to the interactive graphic representation.

繰り返し変動荷重を受ける鋼構造物の弾塑性,有限変形解析

An unified and effective method, which enable one to trace the elasto-plastic; finite deformation behaviors and to evaluate the so-called shake-down limits considered on the geometrical non-linearity, of structures subjected to repeated variable loads, is presented. It is assumed that the domain of the variable loads is given as a hyperpolyhedron and the instantaneous loads move arbitrarily inside the prescribed load domain during the loading time. Likewise, the domains of the the response displacements, strains and stresses of the structures under the above loading are also supposed to be the hyperpolyhedra, vertex of which are the extreme responses corresponding to those of the polyhedric load domain, respectively. Under these assumptions, basic equations governing the relations between the parameter: P^* (which denotes the magnitude of the load domain) and each of the extreme responses, are derived, in which the well-established total Lagrangian formulation is employed to introduce the finite de-formation effects. Elasto-plastic, finite deformation analyses of the plane truss structure composed of 11 members are performed, and show that the present approach might be very advantageous and effective for investigating the plastic-collapse behavior of structures and structural elements, such as offshore structures, under repeated variable loading.