• Title/Summary/Keyword: Stiffness matrix

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Analysis of cable structures through energy minimization

  • Toklu, Yusuf Cengiz;Bekdas, Gebrail;Temur, Rasim
    • Structural Engineering and Mechanics
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    • v.62 no.6
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    • pp.749-758
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    • 2017
  • In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, $P=K{\Delta}$, where P is the load vector, K is the stiffness matrix and ${\Delta}$ is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of non-linear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate.

Structural identification based on substructural technique and using generalized BPFs and GA

  • Ghaffarzadeh, Hosein;Yang, T.Y.;Ajorloo, Yaser Hosseini
    • Structural Engineering and Mechanics
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    • v.67 no.4
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    • pp.359-368
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    • 2018
  • In this paper, a method is presented to identify the physical and modal parameters of multistory shear building based on substructural technique using block pulse generalized operational matrix and genetic algorithm. The substructure approach divides a complete structure into several substructures in order to significantly reduce the number of unknown parameters for each substructure so that identification processes can be independently conducted on each substructure. Block pulse functions are set of orthogonal functions that have been used in recent years as useful tools in signal characterization. Assuming that the input-outputs data of the system are known, their original BP coefficients can be calculated using numerical method. By using generalized BP operational matrices, substructural dynamic vibration equations can be converted into algebraic equations and based on BP coefficient for each story can be estimated. A cost function can be defined for each story based on original and estimated BP coefficients and physical parameters such as mass, stiffness and damping can be obtained by minimizing cost functions with genetic algorithm. Then, the modal parameters can be computed based on physical parameters. This method does not require that all floors are equipped with sensor simultaneously. To prove the validity, numerical simulation of a shear building excited by two different normally distributed random signals is presented. To evaluate the noise effect, measurement random white noise is added to the noise-free structural responses. The results reveal the proposed method can be beneficial in structural identification with less computational expenses and high accuracy.

Analysis of Dynamic Behavior of Flexible Rectangular Liquid Containers by the Coupled Boundary Element-Finite Element Method (경계요소-유한요소 연계법에 의한 구형 수조구조물의 동적거동 특성해석)

  • Koh, Hyun Moo;Park, Jang Ho;Kim, Jaekwan
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.5
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    • pp.1033-1042
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    • 1994
  • Dynamic behavior of flexible rectangular liquid containers is analyzed by a two-dimensional coupled boundary element-finite element method. The irrotational motion of inviscid and incompressible ideal fluid is modeled by boundary elements and the motion of structure by finite elements. A singularity free integral formulation is employed for the implementation of boundary element method. Coupling is performed by using compatibility and equilibrium conditions along the interface between the fluid and structure. The fluid-structure interaction effects are reflected into the coupled equation of motion as added fluid mass matrix and sloshing stiffness matrix. By solving the eigen-problem for the coupled equation of motion, natural frequencies and mode shapes of coupled system are obtained. The free surface sloshing motion and hydrodynamic pressure developed in a flexible rectangular container due to horizontal and vertical ground motions are computed in time domain.

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The Basic Study on Fatigue Crack Growth Behavior of SiC Whisker Reinforced Aluminium 6061 Composite Material (SiC 휘스커 보강 Al 6061 복합재료의 피로균열진전 특성에 관한 기초 연구)

  • 권재도;안정주;김상태
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.9
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    • pp.2374-2385
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    • 1994
  • SiCw/Al composite material is especially attractive because of their superior specific strength, specific stiffness, corrosion fatigue resistance, creep resistance, and wear resistance compared with the corresponding wrought Al alloy. In this study, Fatigue crack growth behavior and fatigue crack path morphology(FCPM) of SiC whisker reinforced Al 6061 alloy with 25% SiC volume fraction and Al 6061 allay were performed. Result of the fatigue crack growth test sgiwed that fatigue crack growth rate of SiCw/Al 6061 composite was slower than that of Al 6061 matrix therefore it was confirmed that Sic whisker have a excellent fatigue resistance. And Al 6061 matrix had only FCPM perpendicular to loading direction. On the other hand SiCw/Al 6061 composite had three types in fatigue crack path morphology. First type is that both sides FCPM of artificial notch are perpendicular to loading direction. Second type is that a FCPM in artifical notch has slant angle to loading direction and the other side FCPM is perpendicular to loading direction. Third type is that both sides FCPM of notch have slant angle to loading direction. It was considered that this kinds of phenomena were due to non-uniform distribution of SiC whisker and confirmed by SEM observation for fracture mechanism study.

A Study on Low Velocity Impact and Residual Compressive Strength for Carbon/Epoxy Composite Laminate (탄소섬유/에폭시 복합적층판의 저속 충격 및 잔류 압축강도에 관한 연구)

  • Lee, S.Y.;Park, B.J.;Kim, J.H.;Lee, Y.S.;Jeon, J.C.
    • Proceedings of the KSME Conference
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    • 2000.11a
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    • pp.250-255
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    • 2000
  • Damage induced by low velocity impact loading in aircraft composite laminates is the form of failure which is occurred frequently in aircraft. Low velocity impact can be caused either by maintenance accidents with tool drops or by in-flight impacts with debris. As the consequences of impact loading in composite laminates, matrix cracking, delamination and eventually fiber breakage for higher impact energies can be occurred. Even when no visible impact damage is observed, damage can exist inside of composite laminates and the carrying load of the composite laminates is considerably reduced. The reduction of strength and stiffness by impact loading occurs in compressive loading due to laminate buckling in the delaminated areas. The objective of this study is to determine inside damage of composite laminates by impact loading and to determine residual compressive strength and the damage growth mechanisms of impacted composite laminates. For this purpose a series of impact and compression after impact tests are carried out on composite laminates made of carbon fiber reinforced epoxy resin matrix with lay up pattern of $[({\pm}45)(0/90)_2]s$ and $[({\pm}45)(0)_3(90)(0)_3({\pm}45)]$. UT-C scan is used to determine impact damage characteristics and CAI(Compression After Impact) tests are carried out to evaluate quantitatively reduction of compressive strength by impact loading.

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A Simplified Finite Element Method for the Ultimate Strengh Analysis of Plates with Initial Imperfections (초기결함을 가진 판의 최종강도해석을 위한 간이 유한요소법)

  • Jeom-K.,Paik;Chang-Y.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.26 no.1
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    • pp.24-38
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    • 1989
  • In this study, an attempt for formulating a new and simplified rectangular finite element having only four corner nodal points is made to analyze the elastic-plastic large deformation behaviour up to the ultimate limit state of plates with initial imperfections. The present finite element contains the geometric nonlinearity caused by both in-plane and out-of-plane large deformation because for very thin plates the influence of the former may not be negligible. Treatment of expanded plastic zone in the plate thickness direction of the element is simplified based upon the concept of plastic node method so that the elastic-plastic stiffness matrix of the element is derived by the simple matrix operation without performing complicated numerical integration. Thus, a considerable saving of the computational efforts is expected. A computer program is also completed based on the present formulation and numerical calculation for some examples is performed so as to verify the accuracy and validity of the program.

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Effect of Composite Sandwich Endplates on the Improvement of Cold Start Characteristics for PEMFC (복합재료 샌드위치 엔드플레이트의 연료전지 냉시동성 향상에 미치는 효과)

  • Suh, Jung-Do;Ko, Jae-Jun;Ahn, Byung-Ki;Yu, Ha-Na;Lee, Dai-Gil
    • Journal of Hydrogen and New Energy
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    • v.22 no.6
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    • pp.859-867
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    • 2011
  • The cold start problem is one of major obstacles to overcome for the commercialization of fuel cell vehicles. However, the cold start characteristics of fuel cell systems are very complicated since various phenomena, i.e. ice-blocking, electro-chemical reactions, heat transfer, and defrosting of BOP components, are involved in them. This paper presents a framework to approach the problem at a full stack scale using Axiomatic Design (AD). It was characterized in terms of Functional Requirements (FRs) and Design Parameters (DPs) while their relations were established in a design matrix. Considering the design matrix, the endplates should have low thermal conductivity and capacity without increase in weight or decrease in structural stiffness. Consequently, composite sandwich endplates were proposed and examined both through finite element analyses and experiments simulating cold start conditions. From the examinations, it was found that the composite sandwich endplates significantly contributed to improving the cold start characteristics of PEMFC.

Bending of steel fibers on partly supported elastic foundation

  • Hu, Xiao Dong;Day, Robert;Dux, Peter
    • Structural Engineering and Mechanics
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    • v.12 no.6
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    • pp.657-668
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    • 2001
  • Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

Fracture Toughness and Slinding Wear Properties of ABOw/AC4CH by Binder Additives (ABOw/AC4CH의 바인더 종류에 따른 파괴인성 및 미끄럼마모 특성)

  • Park, Won-Jo;Jung, Jae-Wook;Choi, Yong-Bum;Lee, Kwung-Young
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.10a
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    • pp.373-378
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    • 2002
  • Metal matrix composites have a great interest in recent years because high specific strength, high specific stiffness characteristics, and application ranges of the composites are extend to variety industry. In this paper, an investigation was performed on the plane strain fracture toughness and slinding wear properties of AC4CH alloy(Al-Si-Mg line) reinforced with 20wt% aluminum borate whisker expect one, which contained a inorganic binder($TiO_2$). the binder led to the formation of strengthen the whisker each other. The test of fracture toughness was using CT(half size) specimen of thickness 12.5mm, width 25mm. and test of slinding wear of using tribo a pin-on-disk machine and lubricant is used without paraffine 8.2CST at room temperature. As results, Fracture toughness $K_{IC}$ is $8.7MPa-m^{05}$ for ABOw/AC4CH, $9.28MPa-m^{05}$ for ABOw/AC4CH added $TiO_2$. but AC4CH alloy was violated the critical stipulated by ASTM standard for valid measurement of $K_{IC}$. In case of, it was performed $J_{IC}$ test instead of $K_{IC}$ based on ASTM E 1820.

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Three-dimensional vibration analysis of 3D graphene foam curved panels on elastic foundations

  • Zhao, Li-Cai;Chen, Shi-Shuenn;Khajehzadeh, Mohammad;Yousif, Mariwan Araz;Tahouneh, Vahid
    • Steel and Composite Structures
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    • v.43 no.1
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    • pp.91-106
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    • 2022
  • This paper has focused on presenting a three dimensional theory of elasticity for free vibration of 3D-graphene foam reinforced polymer matrix composites (GrF-PMC) cylindrical panels resting on two-parameter elastic foundations. The elastic foundation is considered as a Pasternak model with adding a Shear layer to the Winkler model. The porous graphene foams possessing 3D scaffold structures have been introduced into polymers for enhancing the overall stiffness of the composite structure. Also, 3D graphene foams can distribute uniformly or non-uniformly in the shell thickness direction. The effective Young's modulus, mass density and Poisson's ratio are predicted by the rule of mixture. Three complicated equations of motion for the panel under consideration are semi-analytically solved by using 2-D differential quadrature method. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary at the curved edges. It is explicated that 3D-GrF skeleton type and weight fraction can significantly affect the vibrational characteristics of GrF-PMC panel resting on two-parameter elastic foundations.