Simultaneous shape and topology optimization of prestressed concrete beams

This paper presents a new optimization approach for the design of prestressed concrete beams. The prestressing tendon is modeled as a chain of linear segments that transfer point forces to the concrete domain according to the tendon’s angles. The concrete beam is modeled as a discretized continuum following density-based approaches to topology optimization. The shape of the tendon and the topology of the surrounding concrete are optimized simultaneously within a single problem formulation. A special filtering technique is developed in order to ensure that the tendon is covered by concrete, thus shape and topological variables are tightly coupled. Several test cases demonstrate the applicability of the proposed optimization procedure. The deformation of the optimized designs due to external loads is counteracted by the deformation due to prestressing, hence by tuning the force in the tendon the total deformation can approach zero. Consequently, the beams exhibit a compression-only response meaning that the common goal of prestressed concrete design is achieved.     

Determination of design moments in bridges constructed with a movable scaffolding system (MSS)

This paper introduces simple but effective equations to calculate the dead load and tendon moments in concrete box-girder bridges constructed with a movable scaffolding system (MSS). Through time-dependent analyses of concrete box-girder bridges considering the construction sequence and creep deformation of concrete, structural responses related to the member forces are reviewed. On the basis of the compatibility condition and equilibrium equation at every construction stage, basic equations that can describe the moment variation with time in movable scaffolding construction are derived. These equations are then extended to take into account the moment variation according to changes in the construction steps. By using the introduced relations, the design moment and its variation over time can easily be obtained with only the elastic analysis results and without additional time-dependent analyses considering the construction sequences. In addition, the design moments determined by the introduced equations are compared with the results from a rigorous numerical analysis with the objective of establishing the relative efficiencies of the introduced equations.     

An interactive design algorithm for prestressed concrete girders

The primary purpose of this paper is to discuss an interactive design and analysis algorithm for prestressed concrete girders. Prestressed concrete highway bridge girder design is used for the prototype computer program to simplify the incorporation of design code requirements and loading conditions. The computer code can be extended to include other prestressed concrete girder applications. The second purpose arises from the search for the optimum prestressed concrete girder design. Linear programming is discussed as a possible method to arrive at the optimum girder cross-section and prestressing strand design. However, manufacturing standardization and techniques make selection of the optimum crosssection, prestressing force, and strand centroid eccentricity by mathematical methods rather academic. Therefore, design optimization, to be practical, must be based on standard cross-sections and prestressing strand position templates. The algorithm, guided by the engineer, selects, from tabulated standard crosssections and associated combinations of prestressing forces and eccentricities, the cross-section, prestressing force, and eccentricity to satisfy the problem constraints. The kern boundaries are calculated in the analysis portion of the algorithm. The engineer, using the kern boundaries, determines the path of the strands by specifying the strand hold-down points and associated strand centroid eccentricity. The algorithm also provides for shear reinforcement, dead load deflections at transfer and after placement of the slab, and auxiliary nonprestressed tension reinforcement at transfer.     

A CAD-based design parameterization for shape optimization of elastic solids

In this paper a CAD-based design sensitivity analysis (DSA) and optimization method using Pro/ENGINEER for shape design of structural components is presented. The CAD-based design model is critically important for multidisciplinary shape design optimization. Only when each discipline can compute the design sensitivity coefficients of the CAD-based design model, can a true multidisciplinary what-if study, trade-off analysis, and design optimization be carried out. The proposed method will allow the design engineer to compute design sensitivity coefficients of structural performance measures such. as stress and displacement, evaluated using existing finite element analysis (FEA) tools, both h- and p-versions, with respect to design variables defined in the parameterized CAD model. The proposed method consists of (i) a CAD-based design parameterization technique that ties the structural DSA and optimization to a CAD tool; (ii) a design velocity field computation that defines material point movement due to design change in CAD geometry, satisfies linearity and regularity requirements, and supports both hand p-version FEA meshed using existing mesh generators; and (iii) a design optimization method that supports structural geometric and finite element model updates in Pro/ENGINEER during the optimization process.     

Formulation for Reliable Analysis of Structural Frames

Structural engineers use design codes formulated to consider uncertainty for both reinforced concrete and structural steel design. For a simple one-bay structural steel frame, we survey typical uncertainties and compute an interval solution for displacements and forces. The naive solutions have large over-estimations, so we explore the Mullen-Muhanna assembly strategy, scaling, and constraint propagation to achieve tight enclosures of the true ranges for displacements and forces in a fraction of the CPU time typically used for simulations. That we compute tight enclosures, even for large parameter uncertainties used in practice, suggests the promise of interval methods for much larger structures.     

Practical crack control during the construction of precast segmental box girder bridges

Cracks that occurred in the bottom slab of a precast segmental bridge were investigated through a construction sequence analysis, which revealed that the cracks were caused by excessive deformation during temporary post-tensioning while joining the segments. In addition, a parametric study was performed to evaluate the effects of the prestressing sequence, bottom slab thickness, and position of the prestressing anchors. The structural behavior of the girder sections was greatly affected by the thickness of the bottom slab and the position of prestressing anchors, but not by the prestressing sequence. Based on the results, a construction method that prevents the cracks is proposed.     

The cross-section warping effect with the associated creep-induced deformations

The modern bridge girders are of plated character for which the beamtype analysis is inadequate. This is why the three-dimensional approach applying advanced computational analyses must be used to obtain the true 3D structural performance. The paper is directed to the cross section warping effect and to the warping induced long term prestressing loss due to creep of concrete. It is shown that the severity of cross section warping is of fundamental importance, particularly in the case of unevenly distributed and isolated tendons in cross-section and in the case of short spans. Thus it will be appropriate to introduce a new component of the prestress loss – the prestress loss due to creep of concrete induced by cross section warping.     

A parallel aerostructural optimization framework for aircraft design studies

Preliminary aircraft design studies use structural weight models that are calibrated with data from existing aircraft. Computing weights with these models is a fast procedure that provides reliable weight estimates when the candidate designs lie within the domain of the data used for calibration. However, this limitation is too restrictive when we wish to assess the relative benefits of new structural technologies and new aircraft configurations early in the design process. To address this limitation, we present a computationally efficient aerostructural design framework for initial aircraft design studies that uses a full finite-element model of key structural components to better assess the potential benefits of new technologies. We use a three-dimensional panel method to predict the aerodynamic forces and couple the lifting surface deflections to compute the deformed aerodynamic flying shape. To be used early in the design cycle, the aerostructural computations must be fast, robust, and allow for significant design flexibility. To address these requirements, we develop a geometry parametrization technique that enables large geometric modifications, we implement a parallel Newton–Krylov approach that is robust and computationally efficient to solve the aeroelastic system, and we develop an adjoint-based derivative evaluation method to compute the derivatives of functions of interest for design optimization. To demonstrate the capabilities of the framework, we present a design optimization of a large transport aircraft wing that includes a detailed structural design parametrization. The results demonstrate that the proposed framework can be used to make detailed structural design decisions to meet overall aircraft mission requirements.     

Topology optimization of an offshore jacket structure considering aerodynamic,hydrodynamic and structural forces

The present work focused on the optimization of offshore wind turbine structure which can sustain different environmental conditions and is of the least cost. Size and topology optimization is carried out for the jacket structure from the National Renewable Energy Laboratory (NREL) [used in the Offshore Code Comparison Collaboration Continuation (OC4) project] by using teaching learning-based optimization (TLBO) algorithm and genetic algorithm (GA). The optimization process is carried out in Matlab along with the time-dependent dynamic wind turbine simulation with the aerodynamic, hydrodynamic and structural forces in the fatigue, aerodynamics, structures, and turbulence code (FAST) from NREL. This is an innovative process which can be used to substitute the time-consuming construction of a wind turbine for its analysis. In this work, both static and dynamic analyses are carried out for simultaneous size and topology optimization. The forces applied to the structure are realistic in nature and fatigue analysis is carried out to ensure that the structure does not fail during its design life. This ensures that the simulation is more accurate and realistic as compared with other analysis. The results showed that the TLBO algorithm is effective compared to GA in terms of size and topology optimization. Further, the other state-of-the art algorithms from the Congress on Evolutionary Computation (CEC) such as differential evolution, LSHADE, multi-operator EA-II, effective butterfly optimizer, and unified differential evolution are also implemented and the comparative results of all the algorithms are presented.

     

High-fidelity aerostructural optimization with integrated geometry parameterization and mesh movement

This paper extends an integrated geometry parameterization and mesh movement strategy for aerodynamic shape optimization to high-fidelity aerostructural optimization based on steady analysis. This approach provides an analytical geometry representation while enabling efficient mesh movement even for very large shape changes, thus facilitating efficient and robust aerostructural optimization. The geometry parameterization methodology uses B-spline surface patches to describe the undeflected design and flying shapes with a compact yet flexible set of parameters. The geometries represented are therefore independent of the mesh used for the flow analysis, which is an important advantage to this approach. The geometry parameterization is integrated with an efficient and robust grid movement algorithm which operates on a set of B-spline volumes that parameterize and control the flow grid. A simple technique is introduced to translate the shape changes described by the geometry parameterization to the internal structure. A three-field formulation of the discrete aerostructural residual is adopted, coupling the mesh movement equations with the discretized three-dimensional inviscid flow equations, as well as a linear structural analysis. Gradients needed for optimization are computed with a three-field coupled adjoint approach. Capabilities of the framework are demonstrated via a number of applications involving substantial geometric changes.     

Aeroelastic tailoring considering uncertainties in material properties

The robustness of aeroelastic design optimization with respect to uncertainties in material and structural properties is studied both numerically and experimentally. The model consists of thin orthotropic composite wings virtually without fuselage. Three different configurations with consistent geometry but varying orientation of the main stiffness axis of the material are investigated. The onset of aeroelastic instability, flutter, is predicted using finite element analysis and the doublet-lattice method for the unsteady aerodynamic forces. The numerical results are experimentally verified in a low-speed wind tunnel. The optimization problem is stated as to increase the critical air speed, above that of the bare wing by massbalancing. It is seen that the design goals are not met in the experiments due to uncertainties in the structural performance of the wings. The uncertainty in structural performance is quantified through numerous dynamic material tests. Once accounting for the uncertainties through a suggested reformulation of the optimization problem, the design goals are met also in practice. The investigation indicates that robust and reliable aeroelastic design optimization is achievable, but careful formulation of the optimization problem is essential.     

Structural analysis and optimization in the framework of reduced-basis method

This work focus on the implementation and application of Reduced Basis (RB) techniques for structural and sensitivities analysis of trusses, 2D elasticity, heat conduction and coupled thermal–elastic problems. This techniques has been implemented in order to economically and accurately compute outputs and their gradients, as they are calculated several times due to the changes of the parameters in an optimization process. The tools developed here are combined with mathematical programming algorithms and multiobjective strategies to form a robust and reliable optimization procedure to achieve better performance on structural designs. Some simple academic applications have been considered for the validation of all proposed methodologies. Further studies will addressed more complex problems.     

The selection of a system of prestressing tendons in hyperstatic beams as a problem of linear integer programming

The paper deals with a method for the optimum design of prestressing tendons in continuous beams subjected to many load states. The minimum volume of prestressing steel has been assumed as the optimization criterion. Many possible paths of prestressing tendons allowable from the structural point of view have been taken into consideration. The authors have investigated the number of cables in individual paths in order to obtain the minimum value of the objective function. The linear integer optimization method has been used for finding the optimum layout of tendon paths. Use has been made of the IBM mathematical programming system extended procedure package. Theoretical considerations are accompanied by a numerical example.     

A Lagrangian approach for electrostatic analysis of deformableconductors

Deformable conductors are frequently encountered in microelectromechanical systems (MEMS). For example, in electrostatic MEMS, microstructures undergo deformations because of electrostatic forces caused by applied potentials. Computational analysis of electrostatic MEMS requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed by a Lagrangian approach using the undeformed position of the structures. However, the electrostatic analysis is performed by using the deformed position of the conductors. In this paper, we introduce a Lagrangian approach for electrostatic analysis. In this approach, when the conductors undergo deformation or shape changes, the surface charge densities on the deformed conductors can be computed without updating the geometry of the conductors. The Lagrangian approach is a simple, but critical, idea that radically simplifies the analysis of electrostatic MEMS     

On design sensitivities in the structural analysis and optimization of flexible multibody systems

Multibody System Dynamics - The structural analysis and optimization of flexible multibody systems become more and more popular due to the ability to efficiently compute gradients using...     

Numerical shape optimization based on meshless method and stochastic optimization technique

This paper puts forward a newer approach for structural shape optimization by combining a meshless method (MM), i.e. element-free Galerkin (EFG) method, with swarm intelligence (SI)-based stochastic ‘zero-order’ search technique, i.e. artificial bee colony (ABC), for 2D linear elastic problems. The proposed combination is extremely beneficial in structural shape optimization because MM, when used for structural analysis in shape optimization, eliminates inherent issues of well-known grid-based numerical techniques (i.e. FEM) such as mesh distortion and subsequent remeshing while handling large shape changes, poor accuracy due to discontinuous secondary field variables across element boundaries needing costly post-processing techniques and grid optimization to minimize computational errors. Population-based stochastic optimization technique such as ABC eliminates computational burden, complexity and errors associated with design sensitivity analysis. For design boundary representation, Akima spline interpolation has been used in the present work owing to its enhanced stability and smoothness over cubic spline. The effectiveness, validity and performance of the proposed technique are established through numerical examples of cantilever beam and fillet geometry in 2D linear elasticity for shape optimization with behavior constraints on displacement and von Mises stress. For both these problems, influence of a number of design variables in shape optimization has also been investigated.     

Geometric uncertainties in finite element analysis

This paper demonstrates the use of automatic differentiation in solving finite element problems with random geometry. In the area of biomechanics, the shape and size of the domain is often known only approximately. Stochastic finite element analysis can be used to compute the variability in the structural response as a result of variability in the shape of the structural domain. Automatic differentiation can be used to compute the shape sensitivites accurately and effortlessly. Unlike randomness in material properties, the response variability can be the same as or greater than the variability in the input. When both the Young's modulus and geometry are random, it is likely that randomness in geometry will dominate randomness in Young's modulus.     

Parametric modelling and evolutionary optimization for cost-optimal and low-carbon design of high-rise reinforced concrete buildings

Design optimization of reinforced concrete structures helps reducing the global carbon emissions and the construction cost in buildings. Previous studies mainly targeted at the optimization of individual structural elements in low-rise buildings. High-rise reinforced concrete buildings have complicated structural designs and consume tremendous amounts of resources, but the corresponding optimization techniques were not fully explored in literature. Furthermore, the relationship between the optimization of individual structural elements and the topological arrangement of the entire structure is highly interactive, which calls for new optimization methods. Therefore, this study aims to develop a novel optimization approach for cost-optimal and low-carbon design of high-rise reinforced concrete structures, considering both the structural topology and individual element optimizations. Parametric modelling is applied to define the relationship between individual structural members and the behavior of the entire building structure. A novel evolutionary optimization technique using the genetic algorithm is proposed to optimize concrete building structures, by first establishing the optimal structural topology and then optimizing individual member sizes. In an illustrative example, a high-rise reinforced concrete building is used to examine the proposed optimization approach, which can systematically explore alternative structural designs and identify the optimal solution. It is shown that the carbon emissions and material cost are both reduced by 18–24% after performing optimization. The proposed approach can be extended to optimize other types of buildings (such as steel framework) with a similar problem nature, thereby improving the cost efficiency and environmental sustainability of the built environment.     

Unified concepts of constitutive modelling and numerical solution methods for concrete creep problems

In the first part of the paper an internal variable model is developed for concrete creep with the following features: creep strain is a linear functional of stress history; application or removal of stress produces instantaneous elastic response; upon removal of stress, creep deformations partially recover, approaching in the limit an irrecoverable part. The mechanism of each creep component is affected be temperature, humidity and loading age.In the second part the internal state variables are derived from concrete creep data with loading ages ranging from 7 to 4560 days and temperatures from 20° to 95°C. Several aging models are examined for which the parameters are determined via least squares optimization. A root mean square criterion is used to assess the approximation.In the third part a step by step algorithm is developed for incremental solution of the time-dependent creep process, noting that the governing equation of evolution lends itself to an economic computer solution without storing previous results. The one-dimensional constitutive statements are extended to multiaxial conditions and subsequently projected from the local level onto the structural level via finite elements (incremental initial load method).In the fourth part the creep behaviour of a prestressed concrete reactor vessel is examined for a loading history which includes hygrothermal effects due to drying and heating as well as prestress and cycling pressure.