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.     

An improved formulation of space stiffeners

This paper presents a displacement based finite element model for predicting the constraint torsion effect of stiffeners. In structural modelling, the plate/shell and the stiffeners are treated as separate elements where the displacement compatibility transformation between these two types of elements takes into account the constraint torsional warping effect in the stiffeners. The development is based on a general beam theory which includes flexural-torsion coupling, constrained torsion warping, and shear-centre location. The virtual work principle includes the second order terms of finite beam rotations. For finite element analysis, cubic Hermitian polynomials are used as shape functions of the straight space frame element with two nodes. Elastic stiffness and geometric stiffness matrices for an arbitrary cross-section are evaluated in a closed form, and load correction stiffness for eccentric stiffener loads are considered. To demonstrate the importance of torsion warping constraints and to illustrate the accuracy of this formulation, finite element solutions are presented and compared with available solutions.     

Topology optimization of frame structures with flexible joints

A method for structural topology optimization of frame structures with flexible joints is presented. A typical frame structure is a set of beams and joints assembled to carry an applied load. The problem considered in this paper is to find the stiffest frame for a given mass. By introducing design variables for beams and joints, a mass distribution for optimal structural stiffness can be found. Each beam can have several design variables connected to its cross section. One of these is an area-type design variable which is used to represent the global size of the beam. The other design variables are of length ratio type, controlling the cross section of the beam. Joints are flexible elements connecting the beams in the structure. Each joint has stiffness properties and a mass. A framework for modelling these stiffnesses is presented and design variables for joints are introduced. We prove a theorem which can be interpreted as the fact that the removal of structural elements, e.g. joints or beams, can be modelled by a small strictly positive material amount assigned to the element. This is needed for the computations of sensitivities used in the applied gradient based iterative method. Both two and three dimensional problems, as well as multiple load cases and multiple mass constraints, are treated.     

Structural optimization with fatigue and ultimate limit constraints of jacket structures for large offshore wind turbines

The purpose of the research presented in this paper is to develop and implement an efficient method for analytical gradient-based sizing optimization of a support structure for offshore wind turbines. In the jacket structure optimization of frame member diameter and thickness, both fatigue limit state, ultimate limit state, and frequency constraints are included. The established framework is demonstrated on the OC4 reference jacket with the NREL 5 MW reference wind turbine installed at a deep water site. The jacket is modeled using 3D Timoshenko beam elements. The aero-servo-elastic loads are determined using the multibody software HAWC2, and the wave loads are determined using the Morison equation. Analytical sensitivities are found using both the direct differentiation method and the adjoint method. An effective formulation of the fatigue gradients makes the amount of adjoint problems that needs to be solved independent of the amount of load cycles included in the analysis. Thus, a large amount of time-history loads can be applied in the fatigue analysis, resulting in a good representation of the accumulated fatigue damage. A reduction of 40 % mass is achieved in 23 iterations using the CPLEX optimizer by IBM ILOG, where both fatigue and ultimate limit state constraints are active at the optimum.     

Topology optimization of frame structures—joint penalty and material selection

This paper deals with joint penalization and material selection in frame topology optimization. The models used in this study are frame structures with flexible joints. The problem considered is to find the frame design which fulfills a stiffness requirement at the lowest structural weight. To support topological change of joints, each joint is modelled as a set of subelements. A set of design variables are applied to each beam and joint subelement. Two kinds of design variables are used. One of these variables is an area-type design variable used to control the global element size and support a topology change. The other variables are length ratio variables controlling the cross section of beams and internal stiffness properties of the joints. This paper presents two extensions to classical frame topology optimization. Firstly, penalization of structural joints is presented. This introduces the possibility of finding a topology with less complexity in terms of the number of beam connections. Secondly, a material interpolation scheme is introduced to support mixed material design.     

Optimal joint positions and stiffness distribution for minimum mass frames with damping constraints

Optimal design of frames including cross-sectional dimensions (size parameters) and rigid joint positions between beams (configuration parameters) is treated in the paper. The optimal design corresponds to a minimal mass structure with constraints set on damping capacity of free vibration modes. The sensitivity analysis of distinct as well as multiple frequencies is performed analytically using a complex variable sensitivity method. The linking process of size and configuration variables is applied to generate different classes of optimal designs. The numerical algorithm is based on quadratic approximation of the objective function and linear approximation of active constraints. The examples are provided for 2, 12, and 124 beam frames.Presented at WCSMO-2, Zakopane, Poland, May 26–30, 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.     

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.     

A NLP approach for evaluating storey-buckling strengths of steel frames under variable loading

The problem of determining elastic buckling strengths for unbraced steel frames under variable loading is investigated in this paper. Whereas the pattern of applied loads is specified prior to stability analysis of a frame under proportional loading, load patterns are not predefined in variable loading. The conventional methods for evaluating the stability strength of unbraced frames under proportional loading are not applicable for variable loading, since the load pattern is unknown. Taking into account the concept of storey-based buckling, the problem of frame stability under variable loading is presented as a pair of minimization and maximization problems subject to stability constraints, which are solved by a nonlinear programming (NLP) method. The proposed variable loading approach takes into account the variability of applied loads during the life span of the structure, and as such, provides accurate evaluation of elastic frame-buckling strengths.     

Automated optimization of transverse frame layouts for ships by elastic-plastic finite element analysis

This paper presents a model for the optimum design of ship transverse frames. An elastic-plastic finite element analysis algorithm for plane frames has been incorporated in the model to evaluate the ultimate strength of the overall frame, and different effects of design loads. Using these strengths and load effects, appropriate design constraints are then formulated to prevent different failure categories; the overall collapse, ultimate limit state failures and serviceability failures. Possible instabilities and effects of combined loads are accounted for in formulating these constraints. Scantlings of the frame structure have been modelled as free design variables. The weight function and different constraint functions are then derived relating design variables in such a way that once parameters for finite element analysis are input, the scheme automatically forms the objective function and all constraints, and then interacts with the simplex algorithm through sequential linearization to find the optimum solution. Thus the scheme is almost automatic. Different layouts of the frame structure have been designed by executing this scheme, which demonstrates the capability of the model and the possibility of weight savings by choosing the appropriate layout. Finally, it is suggested how this model would interact with the design of longitudinal materials to ensure the overall optimality in ship hull module design, to prevent grillage buckling and to validate underlying assumptions in analysis.     

Computer aided design of unit loads

The unit load design problem includes the selection of the best pallet or container size, the best pallet or container layout, and the best number of parta per pallet or container. Three different approaches to solve the unit load design problem are identified in this paper and a new procedure is proposed: Computer Aided Design of Unit Loads (CADUL I). Using CADUL I, unit loads are designed considering system constraints (i.e., rack opening dimensions, aisle width, trailer-truck container dimensions, product crushability constraints, material handling equipment stacking capability and weight capacity) and a cost function that includes handling, storage, transportation, and pallet or container costs. An example is used to illustrate how CADUL I works and how these approaches to unit load design perform sensitivity analysis to validate the results obtained.     

Neural networks in mechanics of structures and materials – new results and prospects of applications

Basic ideas of back-propagation neural networks (BPNNs) are presented in short. Then BPNN applications in analysis of the following problems are discussed: (1) bending analysis of elastoplastic beams, (2) elastoplastic plane stress problem, (3) estimation of fundamental vibration periods of real buildings, (4) detection of damage in a steel beam, (5) identification of loads applied to an elastoplastic beam. Regularization neural network is briefly discussed and its application to estimation of concrete fatigue durability it shown. A modified Hopfield network is used to the analysis of an elastic angular plate with unilateral constraints. In the end some conclusions and prospects of neurocomputing applications are pointed out.     

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...     

Artificial Bee Colony (ABC) algorithm in the design optimization of RC continuous beams

The objective of this study is to obtain the optimum design for reinforced concrete continuous beams in terms of cross section dimensions and reinforcement details using a fine tuned Artificial Bee Colony (ABC) Algorithm while still satisfying the constraints of the ACI Code (2008). The ABC algorithm used in this paper has been slightly modified to include a Variable Changing Percentage (VCP) that further improves its performance when dealing with members consisted of multiple variables. The objective function is the total cost of the continuous beam which includes the cost of concrete, formwork and reinforcing steel bars. The design variables used are beam width, beam height, number and diameter of: bottom continuous reinforcing bars, bottom cutoff reinforcing bars, top continuous reinforcing bars and top cutoff reinforcing bars as well as the diameter of stirrups. Four RC beams of varying complexity are presented and optimized. The first three beams are used to fine tune the control parameters of the ABC algorithm, whereas the fourth beam was previously optimized by Arafa et al. (J Artif Intell 76–88, 2011) and is presented here to prove the superiority of this relatively new optimization algorithm.     

Multicriteria optimization of cylindrical sandwich shells under combined loads

The paper is about multicriteria optimization of thin-walled cylindrical shells subjected to simple loads, such as axial compression and external pressure, and combined loads (axial compression and pressure). The optimization problem is given as a bicriterial one, with the weight of the shell as the first objective, and the flexibility of the shell as the second. The set of constraints includes the stability condition, strength conditions for each layer, technological and constructional requirements, and so on. Numerical calculations were obtained with the help of the program MOST. MOST is designed to solve multicriteria optimization problems for nonlinear engineering models with discrete and continuous decision variables. In MOST a concept of Pareto optimum is introduced for generating a set of optimal compromise solutions. The best optimal solution must be chosen from the Pareto optimal set with the help of the preference functions. Results of numerical calculations are presented in the form of tables and diagrams.     

Divergence of a rotating shaft with an intermediate support and conservative axial loads

The dynamic behavior of a rotating shaft with an intermediate support and conservative axial loads is analyzed using Euler beam theory and the assumed mode method. The equations of motion are then transformed to the standard form of eigenvalue problems for determining the critical dimensionless rotational speeds and the critical axial loads corresponding to the divergence-type instability of the shaft. Results of numerical simulations are presented for various combinations of support locations, axial loads and rotational speeds.     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.     

Structural topology optimization with constraints on multi-fastener joint loads

This paper addresses an important problem of design constraints on fastener joint loads that are well recognized in the design of assembled aircraft structures. To avoid the failure of fastener joints, standard topology optimization is extended not only to minimize the structural compliance but also to control shear loads intensities over fasteners. It is shown that the underlying design scheme is to ameliorate the stiffness distribution over the structure in accordance with the control of load distributions over fastener joints. Typical examples are studied by means of topology optimization with joint load constraints and the standard compliance design. The effects of joint load constraints are highlighted by comparing numerical optimization results obtained by both methods. Meanwhile, resin models of optimized designs are fabricated by rapid prototyping process for loading test experiments to make sure the effectiveness of the proposed method.     

An optimum preliminary strength design of reinforced concrete frames

An optimization procedure is organized for the preliminary design of a multistory-multibay, moment-resisting reinforced concrete frame. A reduced set of collapse mechanisms are used to define the kinematic constraints, special constraints are defined in order to satisfy building code requirements and practical design considerations. In the proposed optimum preliminary design the total volume of reinforcing steel required by the members of the structure is minimized. A strong column—weak beam design results from the optimization study. An example is presented to illustrate the proposed method.     

Absolute nodal coordinate plane beam formulation for multibody systems dynamics

A new plane beam dynamic formulation for constrained multibody system dynamics is developed. Flexible multibody system dynamics includes rigid body dynamics and superimposed vibratory motions. The complexity of mechanical system dynamics originates from rotational kinematics, but the natural coordinate formulation does not use rotational coordinates, so that simple dynamic formulation is possible. These methods use only translational coordinates and simple algebraic constraints. A new formulation for plane flexible multibody systems are developed utilizing the curvature of a beam and point masses. Using absolute nodal coordinates, a constant mass matrix is obtained and the elastic force becomes a nonlinear function of the nodal coordinates. In this formulation, no infinitesimal or finite rotation assumptions are used and no assumption on the magnitude of the element rotations is made. The distributed body mass and applied forces are lumped to the point masses. Closed loop mechanical systems consisting of elastic beams can be modeled without constraints since the loop closure constraints can be substituted as beam longitudinal elasticity. A curved beam is modeled automatically. Several numerical examples are presented to show the effectiveness of this method.