Strain Energy Of Structure Research Articles

Morphological evolution of heteroepitaxial islands during Stranski–Krastonov growth

Three-dimensional finite element method is used to simulate the formation, self-assembly and shape transition of heteroepitaxial islands during Stranski–Krastonov growth. In the formulation, strain energy, surface energy, surface anisotropy and elastic anisotropy of a cubic lattice structure are taken into account. In the simulations, the SiGe/Si material system is used as a model system. An empirical surface energy as a function of surface orientation is proposed. The minimum energy surfaces are identified based on existing experimental observations. The simulation results show that the coupling of elastic energy relaxation, surface energy anisotropy and elastic anisotropy strongly influences the surface roughening morphology, self-assembly and shape transition of epitaxial islands, resulting in diverse evolution pathways.

TOPOLOGY OPTIMIZATION OF STRUCTURE WITH GLOBAL STRESS CONSTRAINTS BY INDEPENDENT CONTINUUM MAP METHOD

We establish topology optimization model in terms of Independent Continuum Map method (ICM), so as to avoid the difficulties caused by multiple objective functions of compliance, owing to referring to weight as objective function. Using the distorted-strain-energy criterion, we transform stress constraints on all elements into structure strain-energy constraints in global sense. Then, the problem of topological optimum of continuum structure subjected to global strain-energy constraints is formulated and solved. The process of optimization is conducted through three basic steps which include the computation of the minimum strain energy of structure corresponding to the maximum strain-energy under the load case due to prescribing weight constraint, the determination of the allowable strain-energy of structure for every load case by using a formula from our numerical tests, as well as the establishment and solution of optimization model with the weight function due to all allowable strain energies. A strategy that is available to cope with complicated load ill-posedness in terms of different complementary approaches one by one is presented in the present work. Several numerical examples demonstrate that the topology path of transferring forces can be obtained more readily by global strain energy constraints rather than local stress constraints, and the problem of load ill-posedness can be tackled very well by the weighting method with regard to structural strain energy as weighting coefficient.

Aeroelastic Optimization of Adaptive Bumps for Yaw Control

This paper captures the aeroelastic behavior of adaptable bumps on morphing wings using trained neural networks. Parameters of the bump such as the height, size, location, and shape play a major aerodynamic and structural role. Though other issues such as wave drag minimization, boundary layer control are discussed, the primary problem addressed here is the generation of the lateral directional moment. The shape of the bump is optimized so that it produces maximum yaw moment with a minimum actuation energy spent in creating the adaptive bump. The analysis of fluid separation on the airfoil surface due to various types of bumps and its effects on the aerodynamic forces is performed using the computational fluid dynamics (CFD) software FLUENT TM . This analysis is performed at a low speed of Mach 0.3 and at a transonic speed of Mach 0.7. Structural analysis is performed using the finite element software ANSYS TM using a nonlinear beam model of the bump. In order to perform an aeroelastic analysis, the softwares FLUENT and ANSYS have to be interconnected so that the changing aerodynamic pressure with bump deformation is reflected in the structural analysis. Direct coupling of two such numerical codes, one based on CFD and the other based on finite element modeling (FEM), is computationally expensive. Hence, artificial neural networks are trained from these aerodynamic and structural analysis. Two neural networks are trained, one for the aerodynamic pressure and the other for the structural loads and strain energy. These two neural networks serve as an efficient decoupler, that facilitates an aeroelastic optimization procedure to evaluate the best bump shape for maximum drag for providing micro-yaw control while using the minimum actuation energy and minimizing the loss in the lift.

Structural Optimization under Topological Constraint Represented by Homology Groups (4th Report, An Example of Its Application to Topology Optimization by the Use of Density Approach)

In the process of topology optimization, topology of a structure is, in general, changed in succession. In this paper, a method of inferring the change of topology is proposed. This method makes it possible to impose constraint conditions upon topology of the structure. Topological constraint conditions can be expressed by homology groups. As a numerical example, topology of a plate is optimized using an artificial model (the density approach) under topological constraint conditions that (I) the structure is not divided into pieces during the optimization process, and (II) the number of holes is less than or equal to the prescribed number. As a result, it was found that (1) topological constraints were correctly satisfied by the proposed method, (2) the least useful members tend to be removed by topological constraints, and other ones are reinforced, and (3) the strain energy of structures obtained under certain topological constraints is somewhat higher than that of ones without topological constraints.

On nonunique solutions in topology optimization

This paper deals with the problem of non-unique solutions in topology optimization. Depending on the optimization path, the solutions, in other words the topologies of a structure, are different. The nonuniqueness problem in topology optimization is presented in connection with the testing of different lower material mass value bounding functions and the use of different material properties updating functions and different threshold functions. The structure strain energy minimum criterion is applied to find the optimum topology. A comparison of the topologies obtained from the energy criterion point of view is made.

Application of homology theory to topology optimization of three-dimensional structures using genetic algorithm

In the process of topology optimization of structures using genetic algorithms (GA), many structures, which cannot be analyzed by the finite element method (FEM) often appear and deteriorate the performance of GA. In this paper, a new method that gives such unanalyzable structures fitness values based on their topology represented by homology groups (Abelian groups) is proposed. As numerical examples, strain energy of three-dimensional structures consisting of triangular shell elements is minimized using GA. In some cases, the average fitness value of structures obtained by the proposed method is more than 10 times higher than that of an existing method.

Entropy-based method for topological optimization of truss structures

This paper presents an entropy-based topological optimization method for truss structures. To begin with, a group of variables which mean the density distribution of structural strain energy are introduced. By the variables, a bridge between the energy distribution and topological optimization of trusses is constructed so that the problem of searching for optimal topology is transformed into a problem of finding out the optimum distribution of the strain energy. Once, then, the energy distribution is known, the optimal cross-sectional areas of elements are found out. The above two steps are executed in turn till the convergence is reached. Next, the stiffness and strength reliability corresponding to the final topological structure is computed with the reasonable result.

Multiobjective and multilevel optimization for steel frames

A new application of multiobjective and multilevel optimization techniques for steel frames is presented. Two levels: system and element, and two objectives: maximization of the total structural strain energy and minimization of the total structural weight are considered. The constraints of frequency, strength, buckling, displacement and variable-bounds are treated. Using the building codes, AISC–LRFD, AISC Seismic Provisions and Chinese GBJ17–88, formal mathematical formulations are made. A demonstration example shear steel frame under gravity and earthquake loads is given.

DESIGN SENSITIVITY ANALYSIS AND OPTIMAL DESIGN OF COMPOSITE STRUCTURES USING HIGHER ORDER DISCRETE MODELS

This paper deals with the structural optimization of multilaminated composite plate structures of arbitrary geometry and layup, using single layer higher order shear deformation theory discrete models. The structural and sensitivity analysis formulation is developed for a family of C° Lagrangian elements. The design sensitivities of static response for objective and/or constraint functions, such as maximum displacements, stress failure criterion and elastic strain energy, with respect to ply angles and ply thickness are presented. The objectives of the design are the minimization of the structural elastic strain energy, minimization of maximum deflection and/or the minimization of the structure volume. The accuracy and relative performance of the proposed discrete models are compared and discussed among developed elements and alternative models. Several test designs are optimized to show the applicability of the proposed refined discrete models.

Identification of crack size via an energy approach

An energy method for identifying the size of a crack at given location in structures using one measured eigencouple of the cracked structures is presented. The method utilizes the maximum strain energies of the structures both with and without a crack and the additional strain energy induced by the crack to construct the energy balance equation from which the size of the crack is evaluated through an iteration procedure. A pair of measured vibration frequency and mode shape of the cracked structure is used in a free vibration analysis to derive for its maximum strain energy. The maximum inertia force of the cracked structure is then applied to the uncracked structure with known stiffness and the resulting strain energy of the uncracked structure is obtained in a finite element analysis. Fracture mechanics is used to derive for the additional strain energy induced by the crack. Experimental investigations of several cracked free-free beams are performed to validate the proposed method. Examples of the identification of crack sizes for a number of damaged beam structures are given to further illustrate the feasibility and effectiveness of the present method. Overall the results are encouraging showing that the present method has the prospect of becoming an alternative approach for crack size detection.

Relative energies and strain energies of proposed structures for octaphosphorus

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTRelative energies and strain energies of proposed structures for octaphosphorusBenjamin M. Gimarc and D. Scott WarrenCite this: Inorg. Chem. 1993, 32, 9, 1850–1856Publication Date (Print):April 1, 1993Publication History Published online1 May 2002Published inissue 1 April 1993https://doi.org/10.1021/ic00061a050RIGHTS & PERMISSIONSArticle Views98Altmetric-Citations32LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts Get e-Alerts

Optimization of material distribution within isotropic and anisotropic plates using homogenization

The creation of optimum isotropic, single-layered orthotropic and multilayered anisotropic plate topologies was attempted in the present study. Our objective was the minimization of the structural strain energy under volume constraint. The concept of optimal material distribution based on homogenization of a unit microstructure together with sequential linear programming was used to perform the optimization task. The structural response, computed via a finite element analysis, was calculated using first order shear deformation theory in conjunction with a laminated plate finite element. Isotropic and single-layered orthotropic plates were treated as special cases of multilayered anisotropic laminates. The accuracy of the algorithm developed is demonstrated by means of numerical examples. The optimality of the results obtained was verified by performing structural analysis on different same-volume topologies created according to the algorithmic output and comparing the resulting displacement and stress fields.

Comparative compliance of representative lead designs for surface-mounted components

The author provides equations for the directional spring constants for common compliant lead designs on surface-mounted (SM) components. The lead configurations include the straight J-lead, dimpled J-lead, gull-wing lead, butt-lead, (I-lead), and S-bend lead designs. Elastic strain energy methods were applied to determine the effective flexural and torsional spring constants for each representative lead design. Lead stiffness evaluation was performed for different SM components tested using accelerated functional cycling and circuit-board dynamic bending. Comparative compliance data are provided for the chip-carrier J-lead designs in the Phase A IEEE Compliant Lead Task Force mechanical cycling test program. The solder joint cycles-to-failure statistics indicate that significant differences in attachment fatigue performance can be correlated with disparate lead compliance between the tested SM components. The structural models and strain energy formulation presented provide a generalized method for quantifying the compliance of common lead configurations. The resultant spring constants represent mechanical properties of the particular lead design and are independent of the SM package geometry and PCB (printed circuit board) interconnection details. >

Castigliano's Method for Warped Thin Curved Beams

This presentation illustrates the use of Castigliano's theorem to solve problems of thin curved beams of arbitrary cross section loaded out of plane. This theorem, the result of the application of the principle of minimum complementary energy, is treated extensively in textbooks on strength of materials and elasticity. Solutions of statically determinate and indeterminate problems of thin uniform curved beams of any cross section, loaded out of plane (warping included), were previously developed by the author. Solutions of several simultaneous equations are required to solve such problems whereas Castigliano's Theorem requires mostly integration. To apply the theorem, the strain energy of structure is expressed in terms of point forces and distributed loads. Strain energy may be utilized, since for linearly elastic material the value of the complementary energy is identical to that of the strain energy. Two problems, one statically determinate and one statically indeterminate, are solved to illustrate the method.

Mechanical behaviour of femoral bones in bending loading

A series of 33 human femoral bones have been subjected to a four point bending test at high strain rates. Two different failure modes were recognized. A Y shaped fracture at the middle region induced by a pure bending moment yielded a zone of non-linearity at the load vs deformation curve and a higher bending force, more deformation of the structure and higher strain energy to fracture compared with the less frequently occurring oblique fracture at the distal third of the structure resulting in a failure without a ‘plastic’ portion at the load-deformation curve. Estimated values of bending modulus and maximum bending moment based upon a simple uniform beam model showed high correlation coefficients with the experimentally determined values. Scanning electron microscopic examination of the Y fracture showed distortion and void formation of the material at the structural level. This could explain the extensive non-elastic deformation prior to failure.

A force-field study of alkenyl radical ring closure

In accord with stereoelectronic considerations there is a good correlation between the relative rates, regiochemistry, and stereochemistry of ring closure of ω-alkenyl radicals, and the strain energies of transition structures determined by force field calculations.