• Steel and Composite Structures
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• 제39권5호
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• pp.599-614
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• 2021

This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young's and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

• 한국전산구조공학회논문집
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• 제29권3호
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• pp.237-244
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• 2016

본 연구는 재료비선형 문제를 다루기 위한 비선형 MLS 차분법의 정식화 과정을 제시한다. MLS 차분법은 절점모델을 기반으로 고속 미분근사식을 활용하여 지배 미분방정식을 직접 이산화 하는데, 변수를 변위로 일원화한 Navier 방정식을 사용하여 탄성재료 문제를 다룬 기존의 MLS 차분법은 재료의 구성방정식을 별도로 고려할 수 없다. 본 연구에서는 비선형 재료의 구성방정식을 반영할 수 있는 강정식화를 위해 1차 미분근사를 반복 사용하는 겹미분근사를 고안했다. 응력의 발산으로 표현되는 평형방정식을 그대로 이산화하고 Newton 방법을 적용하여 반복계산을 통해 수렴해를 찾는 비선형 알고리즘을 제시했다. 응력 계산과 내부변수의 갱신은 return mapping 알고리즘을 활용하였고, 알고리즘 접선계수(algorithmic tangent modulus)의 적용을 통해 빠르고 안정적인 반복계산이 가능하도록 하였다. 재생성 시험을 통해 겹미분근사의 정당성을 검증했고, 비선형재료에 대한 인장문제의 해석을 통해 개발된 비선형 MLS 차분 알고리즘의 정확성과 안정성을 확인하였다.

• Coupled systems mechanics
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• 제10권6호
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• pp.509-520
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• 2021

Fiber-reinforced concrete (FRC) is a composite material where small fibers made from steel or polypropylene or similar material are embedded into concrete matrix. In a material model each constituent should be adequately described, especially the interface between the matrix and fibers that is determined with the 'bond-slip' law. 'Bond-slip' law describes relation between the force in a fiber and its displacement. Bond-slip relation is usually obtained from tension laboratory experiments where a fiber is pulled out from a matrix (concrete) block. However, theoretically bond-slip relation could be determined from bending experiments since in bending the fibers in FRC get pulled-out from the concrete matrix. We have performed specially designed laboratory experiments of three-point beam bending with an intention of using experimental data for determination of material parameters. In addition, we have formulated simple layered model for description of the behavior of beams in the three-point bending test. It is not possible to use this 'forward' beam model for extraction of material parameters so an inverse model has been devised. This model is a basis for formulation of an inverse model that could be used for parameter extraction from laboratory tests. The key assumption in the developed inverse solution procedure is that some values in the formulation are known and comprised in the experimental data. The procedure includes measured data and its derivative, the formulation is nonlinear and solution is obtained from an iterative procedure. The proposed method is numerically validated in the example at the end of the paper and it is demonstrated that material parameters could be successfully recovered from measured data.

• Structural Engineering and Mechanics
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• 제48권6호
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• pp.849-878
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• 2013

This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.

• 한국전산구조공학회논문집
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• 제13권3호
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• pp.321-328
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• 2000

본 연구는 유한한 회전의 2차항을 고려한 변위장에 기초하여 변곡률을 가지는 비대칭 박벽곡선보의 해석이론을 제시한다. Vlasov의 가정에 의한 연속체의 선형화된 가상일의 원리로부터 총 포텐셜 에너지를 유도하고, 모든 변위 파라미터와 ？ 함수는 도심에서 정의된다. 절점당 8개의 자유도를 가지는 박벽곡선보 요소의 개발 과정에서 3차 Hermitian 다항식이 형상함수로 이용된다. 본 연구의 타당성과 정확도를 입증하기 위하여, 일축대칭 단면을 갖는 포물선과 타원형상의 곡선보를 선택하여 3차원 자유진동해석과 안정성 해석을 수행한다. 그리고 이 결과를 ABAQUS의 쉘 요소에 의한 것과 비교한다.

• 대한기계학회논문집A
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• 제26권6호
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• pp.1099-1106
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• 2002

This paper provides engineering J-integral and crack opening displacement (COD) estimation equations for circumferential through-wall cracked pipes under internal pressure and under combined internal pressure and bending. Based on selected 3-D finite element calculations for the circumferential through-wall cracked pipes under internal pressure using the idealized power law materials, the elastic and plastic influence functions for fully plastic J-integral and COD solutions are found as a function of the normalized crack length and the mean radius-to-thickness ratio. These developed GE/EPRI-type solutions are then re-formulated based on the enhanced reference stress method. Such re-formulation not only provides simpler equations for J-integral and COD estimations, but also can be easily extended to combined internal pressure and bending. The proposed equations are compared with elastic-plastic finite element results using actual stress-strain data, which shows overall excellent agreement.

• Structural Engineering and Mechanics
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• 제62권6호
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• pp.695-702
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• 2017

In this work, a nonlocal zeroth-order shear deformation theory is developed for the nonlinear postbuckling behavior of nanoscale beams. The beauty of this formulation is that, in addition to including the nonlocal effect according to the nonlocal elasticity theory of Eringen, the shear deformation effect is considered in the axial displacement within the use of shear forces instead of rotational displacement like in existing shear deformation theories. The principle of virtual work together of the nonlocal differential constitutive relations of Eringen, are considered to obtain the equations of equilibrium. Closed-form solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state for simply supported and clamped clamped nanoscale beams are determined.

• Structural Engineering and Mechanics
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• 제67권6호
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• pp.629-641
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• 2018

The paper describes the development of a two-dimensional (2D) co-rotational nonlinear beam finite element that includes advanced path-following capabilities for detecting bifurcation instability in elasto-plasticity of steel elements subjected to fire without introducing imperfections. The advantage is twofold: i) no need to assume the magnitude of the imperfections and consequent reduction of the model complexity; ii) the presence of possible critical points is checked at each converged time step based on the actual load and stiffness distribution in the structure that is affected by the temperature field in the elements. In this way, the buckling modes at elevated temperature, that may be different from the ones at ambient temperature, can be properly taken into account. Moreover, an improved displacement predictor for estimating the displacement field allowed significant reduction of the computational cost. A co-rotational framework was exploited for describing the beam kinematic. In order to highlight the potential practical implications of the developed finite element, a parametric analysis was performed to investigate how the beam element compares both with the EN1993-1-2 buckling curve and with experimental tests on axially compressed steel members. Validation against experimental data and numerical outcomes obtained with commercial software is thoroughly described.

• Interaction and multiscale mechanics
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• 제3권3호
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• pp.213-234
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• 2010

A multiscale method is presented for analysis of thin slab structures in which the microstructures can not be reduced to two-dimensional plane stress models and thus three dimensional treatment of microstructures is necessary. This method is based on the classical asymptotic expansion multiscale approach but with consideration of the special geometric characteristics of the slab structures. This is achieved via a special form of multiscale asymptotic expansion of displacement field. The expanded three dimensional displacement field only exhibits in-plane periodicity and the thickness dimension is in the global scale. Consequently by employing the multiscale asymptotic expansion approach the global macroscopic structural problem and the local microscopic unit cell problem are rationally set up. It is noted that the unit cell is subjected to the in-plane periodic boundary conditions as well as the traction free conditions on the out of plane surfaces of the unit cell. The variational formulation and finite element implementation of the unit cell problem are discussed in details. Thereafter the in-plane material response is systematically characterized via homogenization analysis of the proposed special unit cell problem for different microstructures and the reasoning of the present method is justified. Moreover the present multiscale analysis procedure is illustrated through a plane stress beam example.

• Steel and Composite Structures
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• 제23권1호
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• pp.41-51
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• 2017

A $C^0$ FE model developed based on an efficient higher order zigzag theory is used for hygrothermal analysis of laminated composite plates. The $C^0$ FE model satisfies the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of $C^1$ continuity associated with the above plate theory. In the present theory the above mentioned $C^0$ continuity of the present element is compensated in the stiffness matrix formulation by using penalty parameter approach. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature/moisture fields (initial strains) must be consistent with total strain field. Special steps are introduced by field consistent approach (e.g., sampling at gauss points) to compensate this problem. A nine noded $C^0$ continuous isoparametric element is used in the proposed FE model. Comparison of present numerical results with other existing solutions shows that the proposed FE model is efficient, accurate and free of locking.