Topographic optimization using dynamic stiffness for a plate (original) (raw)
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Vibration Analysis and Multi-Objective Optimization of Stiffened Triangular Plate
Volume 8: 26th Conference on Mechanical Vibration and Noise, 2014
In this paper, nonlinear vibration of a triangular shape plate, with several stiffeners, is studied. The governing equation of transversal deflection of the plate, with considering the effects of orthotropic characteristics and external excitation, is analyzed. The ordinary differential equation for the time response of the system, through employing the Galerkin method, is obtained; and the frequency response of the plateshape structure-using the multiple scale method-is determined. A robust genetic-based multi-objective optimization technique is employed to optimize the system's response by finding the optimum values of the geometry and locations of the plate's stiffeners. The influence of various parameters on the optimization results is investigated. According to the results, the optimum design of the stiffeners leads to a better performance of the vibration response.
Discrete thickness optimization of an automobile body by using the continuous-variable-based method
Journal of Mechanical Science and Technology, 2008
Design optimization of an automobile body for dynamic stiffness improvement is presented. The thicknesses of plates consisting of a monocoque body of an automobile are employed as design variables for optimization whose objective is to increase the first torsional and bending natural frequencies. By allotting one design variable to each plate of the body, compared to previous works based on element-wise design variables, the design space of optimization can be reduced to a large extent. Because the present optimization is based on continuous-variable-based algorithms, considering manufacturability of the optimized result, the converged values of plate thicknesses should be approximated to commercially available discrete values. A new straightforward thickness discretization scheme considering design sensitivities and employing a subsequent reduced optimization problem is proposed. The validity of the proposed thickness discretization scheme is verified through numerical experiments.
Volume 3: 16th International Conference on Advanced Vehicle Technologies; 11th International Conference on Design Education; 7th Frontiers in Biomedical Devices, 2014
When designing a vehicle structure, an optimum design is desired because the structure has a significant impact on its performance. The structure impacts other components in the vehicle as well. The designing process usually involves complex iteration. Analyses must be done at the early stage of the vehicle's development (body-in-white) to minimize the amount of parameter changes needed during the late stage of development. Successfully implementing this strategy reduces the time and cost required to develop an effective vehicle structure. A method known as Simple Structural Surfaces can be used to model the vehicle structure as several planar sheets, as well as determine the forces in each sheet. The downside of using this method is that by using it, determining the deflections in the structure is difficult. In order to eliminate this difficulty, the vehicle is modeled as several beam elements instead. In this method, a finite element method is used to numerically solve for the deflections, reaction forces, and internal loading on each element of the structure. This Simple Structural Beam model can be adapted to allow optimization of the static property of the structure bending stiffness. Dynamic properties of the vehicle structure are also examined through vibration analysis, by determining the fundamental natural frequency of the structure. Vibration also has a large impact on the structure's performance. The goal of the research is to obtain a design that will optimize the static and dynamic properties of the vehicle's structure. In the beam elements, the parameters involved are the length, orientation, cross-sectional area, and moment of inertia. The optimizing process is automated and determines the beam dimensions with largest stiffness to weight ratio. The fundamental natural frequency calculated must be distant from the frequency of the engine, as resonance is also a concern for structural performance. Resonance occurs when the natural frequency of the system is equal to the frequency of a connecting component. This increases the amplitude of vibration significantly and is undesirable for any structural design.
Topology optimization of plate structures using a single- or three-layered artificial material model
Advances in Engineering Software, 2001
This paper presents a topology optimization algorithm for Mindlin±Reissner plate structures. Single-and three-layered arti®cial material models are used with the resizing algorithm of Bendsùe and Kikuchi. The objective is to produce the stiffest single-or three-layered plate for a given volume by redistributing the material throughout the plate. Numerical examples are provided to illustrate the process. q
The International Journal of Advanced Manufacturing Technology, 2011
Geometrical optimization of structural components is a topic of high interest for engineers involved with design activities mainly related to mass reduction. The study described in these pages focuses on the optimization of plates subjected to bending for which stiffness is obtained by a pattern of ribs. Although stiffening by means of ribs is a well-known and old technique, the design of ribs for maximum stiffness is often based on practice and experience. Classical optimization methods such as topological, topographical and parametric optimization fail to give an efficient design with a reasonable programming effort, especially when dealing with many and complex constraints. These constraints are both technical and technological. A most promising technique to obtain optimal rib patterns was to define a set of feasible rib trajectories and then to select the subset with the most efficient combinations. The result is not unique and a method to select the optimal patterns is required. In fact, the stiffening effect increases with increasing rib length, but at a greater cost. A trade-off must be found between structural performance and cost: The tools to guide this selection process is the main objective of the paper, with particular attention in evaluating the stiffening due to the presence of beads on the plate with a close link with the production system and possible technological constraints which can occur during manufacturing processes, such as minimum rib distance or the presence of discontinuities or the presence of holes or other elements on the plate. A special tool with enforced rib cross section is considered, and optimal rib deployment has to be found. Numerical examples attached show the methodology and obtainable results.
Computers & Structures, 2002
This paper presents an inverse formulation of eigenvalue problem for optimising the dynamics behaviour of structures. The formulation is applied to one-and two-dimensional finite elements which are commonly used in simulation of real structures. Based on this formulation an algorithm is developed for accurate and efficient modification of structures stiffness and mass characteristics to achieve the desired natural frequencies and interpretation of results in terms of physical design parameters. The proposed algorithm is tested by conducting four case studies and the results are validated against exact solutions.
Curved and Layered Structures, 2021
A research subject in structural engineering is the problem of vibration under a loading object. The two-dimensional (2D) model of a structure under loading is an example. In general, this case uses an object that is given a random frequency, which then causes various changes in shape depending on the frequency model. To determine the difference in performance by looking at the different forms of each mode, modal analysis with ANSYS was used. The samples to be simulated were metal plates with three variations of the model, namely, a virgin metal plate without any holes or stiffness, plates with given holes, and metal plates with stiffness on one side. The model was simulated with modal analysis, so that 20 natural frequencies were recorded. The sample also used different materials: low-carbon steel materials (AISI 304), marine materials (AISI 1090), and ice-class materials (AR 235). Several random-frequency models proved the deformation of different objects. Variations of sheet-meta...
Structural topology and shape optimization for a frequency response problem
Computational Mechanics, 1993
A topology and shape optimization technique using the homogenization method was developed for stiffness of a linearly elastic structure by Bendsoe and Kikuchi (1988), Suzuki and Kikuchi (1990, 1991), and others. This method has also been extended to deal with an optimal reinforcement problem for a free vibration structure by Diaz and Kikuchi (1992). In this paper, we consider a frequency response optimization problem for both the optimal layout and the reinforcement of an elastic structure. First, the structural optimization problem is transformed to an Optimal Material Distribution problem (OMD) introducing microscale voids, and then the homogenization method is employed to determine an equivalent "averaged" structural analysis model. A new optimization algorithm, which is derived from a Sequential Approximate Optimization approach (SAO) with the dual method, is presented to solve the present optimization problem. This optimization algorithm is different from the CONLIN (Fleury 1986) and MMA (Svanderg 1987), and it is based on a simpler idea that employs a shifted Lagrangian function to make a convex approximation. The new algorithm is called "Modified Optimality Criteria method (MOC)" because it can be reduced to the traditional OC method by using a zero value for the shift parameter. Two sensitivity analysis methods, the Direct Frequency Response method (DFR) and the Modal Frequency Response method (MFR), are employed to calculate the sensitivities of the object functions. Finally, three examples are given to show the feasibility of the present approach.