• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.7
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• pp.2661-2669
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• 2010

In this study, a finite element formulation based first-order shear deformation theory is developed for non-linear behaviors of laminated composite plates containing matrix cracking. The multi-directional stiffness degradation is developed for adopting the stiffness variation induced from matrix cracking, which is proposed by Duan and Yao. The matrix cracking can be expressed in terms of the variation of material properties, such as Young's modulus, shear modulus and Possion ratio of plates, and sequently it is possible to predict the variation of the local stiffness. Using the assumed natural strain method, the present shell element generates neither membrane nor shear locking behavior. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear or geometrical nonlinear analysis of laminated composite plates. The results of laminated composite plates with matrix cracking may be the benchmark test for the non-linear analysis of damaged laminated composite plates.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.699-702
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• 2000

In order to use a parallel device fur machine tool feed mechanism, it is very important to analyze its stiffness over the workspace. Generally, the stiffness of a rod varies with its length. In this paper, the stiffness of the leg is modeled as a linear function. With the linear stiffness model, the methods that can determine stiffness bounds and max/min stiffness directions are presented utilizing eigenvalues and eigenvectors of the stiffness matrix. The stiffness variation along a tool-path and stiffness mapping over a workspace are presented with cubic-shaped parallel device which is originally designed for machine tool feed mechanism.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.345-352
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• 2001

Derivation procedures of exact static element stiffness matrix of shear deformable thin-walled straight beams are rigorously presented for the spatial buckling analysis. An exact static element stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The buckling loads are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.435-442
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• 2001

Derivation procedures of exact dynamic element stiffness matrix of shear deformable nonsymmetric thin-walled straight beams are rigorously presented for the spatial free vibration analysis. An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The natural frequencies are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.385-392
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• 2002

Derivation procedures of exact elastic element stiffness matrix of thin-walled curved beams are rigorously presented for the static analysis. An exact elastic element stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The displacement and normal stress of the section are evaluated and compared with thin-walled straight and curved beam element or results of the analysis using shell elements for the thin-walled curved beam structure in order to demonstrate the validity of this study.

• Steel and Composite Structures
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• v.24 no.1
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• pp.53-63
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• 2017

The paper presents the simplified matrix stiffness method for analysis of composite and prestressed beams. The method is based on the previously developed "exact" analysis method that uses the mathematical theory of linear integral operators to derive all relations without any mathematical simplifications besides inevitable idealizations related to the material rheological properties. However, the method is limited since the closed-form solution can be found only for specific forms of the concrete creep function. In this paper, the authors proposed the simplified analysis method by introducing the assumption that the unknown deformations change linearly with the concrete creep function. Adopting this assumption, the nonhomogeneous integral system of equations of the "exact" method simplifies to the system of algebraic equations that can be easily solved. Therefore, the proposed method is more suitable for practical applications. Its high level of accuracy in comparison to the "exact" method is preserved, which is illustrated on the numerical example. Also, it is more accurate than the well-known EM method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.423-437
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• 2013

Complex structures are usually assembled from several substructures with joints connecting them together. These joints have significant effects on the dynamic behavior of the assembled structure and must be accurately modeled. In structural analysis, these joints are often simplified by assuming ideal boundary conditions. However, the dynamic behavior predicted on the basis of the simplified model may have significant errors. This has prompted the researchers to include the effect of joint stiffness in the structural model and to estimate the stiffness parameters using inverse dynamics. In the present work, structural joints have been modeled as a pair of translational and rotational springs and frequency equation of the overall system has been developed using sub-structure synthesis. It is shown that using first few natural frequencies of the system, one can obtain a set of over-determined system of equations involving the unknown stiffness parameters. Method of multi-linear regression is then applied to obtain the best estimate of the unknown stiffness parameters. The estimation procedure has been developed for a two parameter joint stiffness matrix.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.57-64
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• 1994

The purpose of this paper is to find minimum surface shape of pneumatic structure using the finite element method. The pneumatic membrane structure is a kind of large deformation problem and very flexible composite material, which mean geomatric nonlinearity. It is not to resist for compression and resultant moment. As the displacement due to internal pressure is getting bigger, it should be considered the direction of forces. It becomes non-linear problem with the non-conservative force. The follower-force depends on the deformation and the direction of force is normal to each element. The solution process is obtained the new stiffness matrix (load correction matrix) depending on deformation through each iterated step. However, the stiffness matrix have not the symmetry and influence on the time of covergence. So in this paper Newton-Rhapson method for solving non-linear problem and for using symmetic matrix, the load direction is changed in each iterated step using the transformation matrix.

• Structural Engineering and Mechanics
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• v.72 no.5
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• pp.617-629
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• 2019

Based on the finite element method of traditional straight Euler-Bernoulli beams and the coupled relations between linear displacement and angular displacement of a pre-twisted Euler-Bernoulli beam, the shape functions and stiffness matrix are deduced. Firstly, the stiffness of pre-twisted Euler-Bernoulli beam is developed based on the traditional straight Euler-Bernoulli beam. Then, a new finite element model is proposed based on the displacement general solution of a pre-twisted Euler-Bernoulli beam. Finally, comparison analyses are made among the proposed Euler-Bernoulli model, the new numerical model based on displacement general solution and the ANSYS solution by Beam188 element based on infinite approach. The results show that developed numerical models are available for the pre-twisted Euler-Bernoulli beam, and which provide more accurate finite element model for the numerical analysis. The effects of pre-twisted angle and flexural stiffness ratio on the mechanical property are investigated.