Design program for multi-story structures

An efficient and short computer program, STFRD, has been developed to facilitate the structural engineer who is involved in multi-story building design. The program consists of three basic parts. The first part of the program performs a preliminary analysis of a frame section of a building using approximate methods to determine forces due to the loads. The loads will consist of uniform dead, live and wind loads. The second part of the program utilizes an iterative process, using the allowable stresses given by the AISC building specifications, to determine member sizes. The third part of the program consists of a matrix analysis of the frame section to determine actual forces on the members, due to the loads. This analysis is used in conjunction with the AISC building codes to verify the adequacy of the member sizes chosen. The program also has a redesign capability which is used if the preliminary member sizes are not adequate. The entire procedure has been programmed for use on a UNIVAC 1108 computer, FORTRAN IV language. The program may be obtained from the author.     

Modified iterated simulated annealing algorithm for structural synthesis

A new hybrid simulated annealing method is presented for the optimization of structural systems subjected to dynamic loads. The optimization problem is formulated as a structural weight minimization, with time-varying constraints on floor displacements, velocities, accelerations, or floor drifts, and structural member combined stresses. In addition, time-invariant constraints on structural frequencies and member sizes that will satisfy the strong column–weak beam philosophy of the building codes can be imposed. The method uses elements of existing simulated annealing algorithms and introduces certain new procedures. Firstly, the search range is automatically reduced, by using the updated information of the current design, at each iteration. Secondly, the inner and outer iteration loops are implemented. Thirdly, sensitivity analysis of the time-varying global displacements is performed with respect to the design variables that are the structural member cross-sectional areas. The results of the sensitivity analysis identify which design variables must be modified to decrease the global displacements in the most effective manner. However, once the variables are identified from the sensitivity analysis, the new values of these variables are determined in a random manner. The possibility of attaining a global minimum is thus maintained. The method is suited for structural optimization problems with time-varying constraints because the annealing is a random search technique and can locate global rather than local minima.     

Computerized automatic design of concrete buildings

The salient features of the AMECO system of integrated computer programs are described. The entire structural design process, from geometry generation in 2- or 3-dimensional, load calculations, etc., to productionof construction documents is computerized in to one operation. Using English language commands, the engineer inputs basic parameters, such as name of the building code, number of stories, floor required to seismic factor, typical member lengths and their connectivities. As few as 16 commands are live loads, design a building of 2000 members. Optional commands are available to input predetermined data or to modify the automatic design procedures.The results of two analyses of a 30 storey frame are presented, one using AMECO with its automatic simulation of the construction sequence, and the second one, using a stiffness matrix program. The latter analysis shows substantial discrepancies in column axial strains and girder moments, demonstrating the potential dangers in use of stiffness matrix programs for structures with high dead loads, such as tall buildings. AMECO utilizes a relaxation method for frame analysis, which produces exact, in-core solutions of a 2000 member building in less than 30 sec on a CDC 6600 computer using 33,000 words of memory.     

Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques

Topology optimization methods using discrete elements such as frame elements can provide useful insights into the underlying mechanics principles of products; however, the majority of such optimizations are performed under deterministic conditions. To avoid performance reductions due to later-stage environmental changes, variations of several design parameters are considered during the topology optimization. This paper concerns a reliability-based topology optimization method for frame structures that considers uncertainties in applied loads and nonstructural mass at the early conceptual design stage. The effects that multiple criteria, namely, stiffness and eigenfrequency, have upon system reliability are evaluated by regarding them as a series system, where mode reliabilities can be evaluated using first-order reliability methods. Through numerical calculations, reliability-based topology designs of typical two- or three-dimensional frames are obtained. The importance of considering uncertainties is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs.     

A minimal mass deployable structure for solar energy harvesting on water canals

This paper produces a design for a minimal mass, deployable support structure for a solar panel covering of water canals. The results are based upon the minimal mass properties of tensegrity structures. The efficient structure is a tensegrity system which has an optimal complexity (i.e. an optimal number of members) for minimal mass. This optimal complexity is derived in this paper, along with deployable schemes which are useful for construction, repairs, for Sun following, and for servicing. It is shown that the minimal structure naturally has deployable features so that extra mass is not needed to add the multifunctional features. The design of bridge structures with tensegrity architecture will show an optimal complexity depending only on material choices and external loads. The minimization problem considers a distributed load (from weight of solar panels and wind loads), subject to buckling and yielding constraints. The result is shown to be a Class 1 Tensegrity substructure (support structure only below the deck). These structures, composed of axially-loaded members (tension and compressive elements), can be easily deployable and have many port-able applications for small spans. The focus of this paper is an application of these minimal mass tensegrity concepts to design shading devices to prevent or reduce evaporation loss, while generating electric power with solar panels as the cover. While the economics of the proposed designs are far from finalized, this paper shows a technical solution that uses the smallest material resources, and shows the technical feasibility of the concept.     

Nonlinear analysis of frames with member unloading

A nonlinear, collapse load analysis that can easily be used to model and accurately predict failure load of braced, structural steel frameworks is formulated. The methodology considers member post-failure, inelastic unloading due to instability, excessive deformation and yielding without placing restrictions on frame size, geometry, or member stress-strain relationships. The loading is so incremented that each load level corresponds to the occurrence of an event, such as formation of a plastic hinge or member instability, and to obtain the correct equilibrium configuration up to collapse, the complete incremental loading history of the structure is taken into account. Moreover, convergence complications associated with limit point instability analyses are avoided, as member-structure deformation compatibility relations are developed and utilized in evaluating member forces from member post-buckling force equilibrium conditions. Illustrative examples are provided to demonstrate the effects of element failure and of bracing system on frame capacity. Lastly, conclusions are drawn as to when a nonlinear analysis beyond bracing failure is warranted and how member unloading affects overall collapse.     

On design of joint positions for minimum mass 3D frames

An iterative procedure for determining the joint positions and dimensions of cross-sections corresponding to a minimum mass space frame is presented. Stress constraints, displacement constraints and side constraints are taken into account, with the possibility for linking of the design variables, which in addition to the joint positions are the beam dimensions. The frame is assumed to carry consecutively a number of different systems of loads, including temperature loads and weights. The stressed state analysis includes tension, bending, shear and torsion of the beam elements. The optimization iteration includes a sequence of quadratic programming problems with the possibility of move-limits. Only “nearby” constraints (active strategy) are considered, and analytical expressions for the gradients are derived. Illustrative medium scale problems are presented.     

Analysis/design of multistory concrete buildings on microcomputers

A computer-aided, integrated, interactive system is developed for the analysis and design of high-rise concrete buildings under vertical, wind and earthquake loads on microcomputers. This system fulfills the need for: new approaches for input and output efficiency as they affect design operation, communication between users and hardwares, problem verification when large scale data input is involved. The system presented has several advantages: no restrictions are imposed on the number of buildings to be solved in the same run, it is a “user-friendly” system, it is interactively implemented, it requires no particular type of professional, it runs with any boundary condition, a typical run can be: analysis then design, or analysis only, or design only. Also, the input data can be checked very easily. In this manner, every participant in a project will provide a share towards this integration with no need to repeat work unnecessarily.Two phases are included. In the first one, geometry is computed or revised, eight loading cases in addition to wind and earthquake loads are considered and only analysis is conducted. In the second phase, the design is done with five options for every section. Members under concentric or eccentric loads, flexure, combined shear and torsion, combined shear and diagonal tension are considered.With the present system, two high-rise buildings were analyzed and designed. The first buildings three different shear walls and is subjected to wind loads. The second building is composed of interconnected frames and is under earthquake loads.     

Exact analytical theory of topology optimization with some pre-existing members or elements

This note deals with topological optimization of structures in which some members or elements of given cross-section exist prior to design and new members are to be added to the system. Existing members are costless, but new members and additions to the cross-section of existing members have a non-zero cost. The added weight is minimized for given behavioural constraints. The proposed analytical theory is illustrated with examples of least-weight (Michell) trusses having (a) stress or compliance constraints, (b) one loading condition and (c) some pre-existing members. Different permissible stresses in tension and compression are also considered. The proposed theory is also confirmed by finite element (FE)-based numerical solutions.     

Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties

This paper discusses a new structural optimization method, based on topology optimization techniques, using frame elements where the cross-sectional properties can be treated as design variables. For each of the frame elements, the rotational angle denoting the principal direction of the second moment of inertia is included as a design variable, and a procedure to obtain the optimal angle is derived from Karush–Kuhn–Tucker (KKT) conditions and a complementary strain energy-based approach. Based on the above, the optimal rotational angle of each frame element is obtained as a function of the balance of the internal moments. The above methodologies are applied to problems of minimizing the mean compliance and maximizing the eigen frequencies. Several examples are provided to show the utility of the presented methodology.     

On design of joint positions for minimum mass 3D frames

An iterative procedure for determining the joint positions and dimensions of cross-sections corresponding to a minimum mass space frame is presented. Stress constraints, displacement constraints and side constraints are taken into account, with the possibility for linking of the design variables, which in addition to the joint positions are the beam dimensions. The frame is assumed to carry consecutively a number of different systems of loads, including temperature loads and weights. The stressed state analysis includes tension, bending, shear and torsion of the beam elements.The optimization iteration includes a sequence of quadratic programming problems with the possibility of move-limits. Only nearby constraints (active strategy) are considered, and analytical expressions for the gradients are derived. Illustrative medium scale problems are presented.     

Automated design of tier buildings

A computer program for the automated design of frameworks in steel tier buildings is described and demonstrated. The design process commences with the input of any initial set of member sies for a given geometry: it is not necessary to begin with good estimates. Cyclic analyses of the building frame and revisions of member sizes then follow. The three-dimensional analysis of the building frame includes the effects of the finite dimensions of moment-resisting connections.

Within each cycle of design, wide-flange members are selected on the basis of satisfying the dead- and live-load stress requirements of the 1969 AISC Specification for Structural Steel in Buildings. Each member is then checked for the most critical combination of vertical and lateral loading. The lightest satisfactory size within a prespecified range of sizes is ultimately selected. The output consists of beam and column schedules that show the final sizes and the design conditions leading to their selection.

Sample three-story and twenty-story building designs show consistent and rapid convergence to a final design without human intervention between consecutive cycles. With highrise buildings becoming increasingly prevalent, an economical automated design procedure should be of great value to the practicing structural engineer.     

CAE技术在汽车座椅骨架开发中的应用

为提高汽车座椅骨架的开发质量,在某型汽车座椅骨架开发中应用CAE技术进行骨架静强度和疲劳等模拟.采用壳单元与梁单元相结合建立座椅骨架有限元模型;根据座椅骨架台架耐久试验要求和试验条件,对座椅安装孔进行全约束处理,并在试验加载位置施加相应的载荷;采用Abaqus/Standard分析座椅骨架强度;在静强度分析基础上应用F...     

Optimal topology design of structures under dynamic loads

When elastic structures are subjected to dynamic loads, a propagation problem is considered to predict structural transient response. To achieve better dynamic performance, it is important to establish an optimum structural design method. Previous work focused on minimizing the structural weight subject to dynamic constraints on displacement, stress, frequency, and member size. Even though these methods made it possible to obtain the optimal size and shape of a structure, it is necessary to obtain an optimal topology for a truly optimal design. In this paper, the homogenization design method is utilized to generate the optimal topology for structures and an explicit direct integration scheme is employed to solve the linear transient problems. The optimization problem is formulated to find the best configuration of structures that minimizes the dynamic compliance within a specified time interval. Examples demonstrate that the homogenization design method can be extended to the optimal topology design method of structures under impact loads.Presented at WCSMO-2, held in Zakopane, Poland, 1997     

A computer program for three dimensional analysis of buildings

A special purpose computer program for the linear three dimensional analyses of building structures for gravity, lateral and earthquake loads is presented. The building is idealized as consisting of a series of rigid jointed rectangular frame or frame-shearwall substructures interconnected through a rigid floor diaphragm. Finite joint sizes, shear deformations and axial deformation of columns are considered. Three dimensional frequencies and mode shapes are evaluated and a response spectrum approach is used for the dynamic analysis. A front-end processor accepts input data in a conversational mode and in free format. Data input is speeded up by taking advantage of the repetitive nature of frame dimensions, member sizes and loadings.     

An efficient approximate analysis method based on an exact univariate model for the element loads

Approximate analysis modules for structural design are usually based on a linear Taylor expansion of the nodal displacements in terms of the reciprocals of the design variables. Direct approximations of the member forces have received lesser attention. This paper describes an approach for the direct calculation of the member forces in a truss as a function of the design variables. It is based on the exact expression of the member forces if only one design variable is allowed to vary at a time. In the case of an arbitrary move in the design space the method gives approximate results of a very good quality. This is obtained by enforcing zero order homogeneity of the element loads and by refining the results via a virtual work equation. The method is illustrated with numerical results on previously published test cases for elastic trusses. Preliminary results for an elastic frame are also presented. This new approximate force model is shown to yield excellent results.     

Modal disparity enhancement through optimal insertion of nonstructural masses

Stiffness variation can be generated in a structure by the systematic application and removal of tension in cables connecting points in the structure. This strategy has been shown to result in modal disparity, a property of the combined structure and cable system that allows vibration energy to flow from one set of modes to another. This facilitates the design of simplified strategies for modal control of flexible structures using only a few selected modes. For some structures, however, cable tension switching may not result in sufficient modal disparity, and, in such cases, the rate of energy transfer across modes may not be sufficient to ensure rapid vibration suppression. Here, it is shown that such difficulty can be alleviated by the insertion of a few nonstructural masses. A procedure is outlined for determining the optimal location of these masses. Simulation results are presented to illustrate vibration control in a 3-D frame.     

Frame Sequential Interpolation for Discrete Level‐of‐Detail Rendering

In this paper we present a method for automatic interpolation between adjacent discrete levels of detail to achieve smooth LOD changes in image space. We achieve this by breaking the problem into two passes: We render the two LOD levels individually and combine them in a separate pass afterwards. The interpolation is formulated in a way that only one level has to be updated per frame and the other can be reused from the previous frame, thereby causing roughly the same render cost as with simple non interpolated discrete LOD rendering, only incurring the slight overhead of the final combination pass. Additionally we describe customized interpolation schemes using visibility textures. The method was designed with the ease of integration into existing engines in mind. It requires neither sorting nor blending of objects, nor does it introduce any constrains in the LOD used. The LODs can be coplanar, alpha masked, animated, impostors, and intersecting, while still interpolating smoothly.     

3D input for CAAD systems

It is often acknowledged that the main advantage of computer aided architectural design (CAAD) systems is that they can be used by architects to quickly and accurately evaluate alternative design solutions using a variety of performance measures which would be too time consuming to apply by hand calculation.To gain the full advantage of interactive CAAD requires the architect to use a computer terminal with graphic capabilities so that he can create and modify his design geometry in a form which can also be directly interpreted by the evaluate routines within the CAAD system. However, it is suggested that it is often difficult for the user of such conventional, graphic, CAAD systems to conceptualise the building being designed by only inspecting and manipulating drawings displayed on the terminal screen.This problem may be accentuated when building users who are not professional architects wish to use a CAAD system so as to participate in the design process.A computerised building block system (BBS) is proposed with which the designer can physically build a model of his design as he would if he was using ‘Lego’¹ blocks. Such a physical representation may allow him to evaluate many of the visual and spatial qualities of his design in a more direct way than could be achieved using computer graphics. However, because the electronic system can ‘read’ the arrangement of blocks and input this information into a computer, the user's design can be evaluated with the same performance measures that are used in existing CAAD systems.     

Application of Micro-GA for optimal cost base isolation design of bridges subject to transient earthquake loads

Seismic isolation and energy dissipation systems are innovative strategies for seismic design and upgrade or retrofit of bridges. In a retrofit design, base isolation devices can be easily incorporated into existing bridges to replace conventional bearings and to improve the overall structural performance. In this paper, an optimal cost base isolation design or retrofit design method for bridges subject to transient earthquake loads is studied. The goal of this study is to push forward the concept of retrofit design optimization of structures using this isolation design as an example. This is achieved by combining nonlinear time history analyses with an optimization procedure to select base isolators that minimize the cost of the isolation system while satisfying certain design requirements. An improved genetic algorithm (GA), Micro-GA, is employed to search for the optimal solutions for such discrete optimization problems. An example of the optimal design of a highway bridge is presented and the minimum cost expense of the isolation system is achieved with improved structural response under multiple transient earthquake loads.