• Journal of the Korean Wood Science and Technology
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• v.37 no.2
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• pp.128-136
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• 2009

Curved glued laminated timber (glulam) is rapidly coming into the domestic modern timber frame buildings and predominant in building construction. The radial stress is frequently occurred in curved beams and is a critical design parameter in curved glulam. Three models, Wilson equation, Exact solution and Approximation equation were introduced to determine the radial stress of curved glulam under pure bending condition. It is obvious that radial stress distribution between small radius and large radius was different due to slight change of neutral plane location to center line. If the beam design with extremely small radius, it should be considered to determine the exact location of maximum radial stress. The current standard KSF 3021 was reviewed and would be considered some adjustment determining the optimum radius in curved glulam. Current design principle is that the stress factor is given by the curvature term only in constant depth of the beam, but like tapered or small radius of beams, the stress factor by Wilson equation was underestimated. So current design formula should be considered to improvement for characterizing the radial stress factor under pure bending condition.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.17-24
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• 1995

This work proposes an optimality criteria applicable to the optimum design of plane frames. Stress constraints as well as displacement constraints are treated as behavioural constraints and thus the first order approximation of stress constraints is adopted. The design space of practical reinforced concrete frames with discrete design variables has been found to have many local minima, and thus it is desirable to find in advance the mathematical minimum, hopefully global, prior to starting to search a practical optimum design. By using the mathematical minimum as a trial design of any search algorithm, we may not full into a local minimum but apparently costly design. Therefore this work aims at establishing a mathematically rigorous method ⑴ by adopting first-order approximation of constraints, ⑵ by reducing the design space whenever minimum size restrictions become "active" and ⑶ by the of Newton-Raphson Method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.7 s.166
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• pp.1205-1214
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• 1999

A new quadrilateral plane stress element is developed for efficient and accurate analysis of thermal stress problems. It is convenient to use the same mesh and the same shape functions for thermal analysis and stress analysis. But, because of the inconsistency between deformation related strain field and thermal strain field, oscillatory responses and considerable errors in stresses are resulted in. To avoid undesired oscillations, strain approximation is enhanced by supplementing several assumed strain terms based on the variational principle. Thermal deformation is incorporated into the generalized mixed variational principle for displacement, strain and stress fields, and basic equations for the modified enhanced assumed strain method are derived. For the stress approximation of bilinear elements, the $5{\beta}$ version of Pian and Sumihara is adopted. The numerical results for several problems show that the present element behaves well and reduces oscillatory responses. it also results in almost the same magnitude of error as compared with the quadratic element.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1429-1437
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• 1992

A new finite element formulation based on the relaxation type hereditary integral is presented for a time-domain analysis of isotropic, linear viscoelastic problems. The semi-discrete variational approximation and elastic-viscoelastic correspondence principle are used in the theoretical development of the proposed method. In a time-stepping procedure of final, linear algebraic system equations, only a small additional computation for past history is required since the equivalent stiffness matrix is constant. The viscoelasticity matrices are derived and the stress computation algorithm is given in matrix form. The effect of time increment and Gauss point numbers on the numerical accuracy is examined. Two dimensional numerical examples of plane strain and plane stress are solved and compared with the analytical solutions to demonstrate the versatility and accuracy of the present method.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.1-19
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• 2016

In this study, the supersonic panel flutter of doubly curved composite sandwich panels with variable thickness is considered under aerothermoelastic loading. Considering different radii of curvatures of the face sheets in this paper, the thickness of the core is a function of plane coordinates (x,y), which is unique. For the first time in the current model, the continuity conditions of the transverse shear stress, transverse normal stress and transverse normal stress gradient at the layer interfaces, as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the sandwich panel are satisfied. The formulation is based on an enhanced higher order sandwich panel theory and the vertical displacement component of the face sheets is assumed as a quadratic one, while a cubic pattern is used for the in-plane displacement components of the face sheets and the all displacement components of the core. The formulation is based on the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear approximation, the one-dimensional Fourier equation of the heat conduction along the thickness direction, and the first-order piston theory. The equations of motion and boundary conditions are derived using the Hamilton principle and the results are validated by the latest results published in the literature.

• Steel and Composite Structures
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• v.27 no.1
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.467-480
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• 2007

Two methods were developed for analyzing problems with two adjacent sub-domains modeled by different kinds of elements in finite element method. Each sub-domain can be defined independently without the consideration of equivalent division with common nodes used for the interface. These two methods employ an individual interface to accomplish the compatibility. The MLSA method uses the moving least square approximation which is the basic formulation for Element Free Galerkin Method to formulate the interface. The displacement field assumed by this method does not pass through nodes on the common boundary. Therefore, nodes can be chosen freely for this method. The results show that the MLSA method has better approximation than traditional methods.

• Computational Structural Engineering
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• v.9 no.2
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• pp.121-131
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• 1996

This work proposes an optimality criteria applicable to the optimum design of plane frames subject to multiple behavioral constraints on member stresses and lateral displacements of nodes and also to side constraints on design variables. The method makes use of a first order approximation for both deflection and stress constraints instead of the zero order approximation based on the concept of FSD (fully stressed design). A redesign algorithm is derived from a mathematically rigorous method which uses the Newton-Raphson method to solve the system of nonlinear constraint equations and reduces the design space whenever minimum size restrictions become active. When applied to worked examples it proved more accurate and efficient, and it is often found that optimum designs are not fully stressed designs. This fact suggests that this rigorous method is worth what it claims for complicated computing and thus had better replace the crude stress ratio algorithm adopted by the majority of optimality criteria approaches. This is particularly true as long as we enjoy ever-increasing computing power at negligible costs.

• Journal of the korean Society of Automotive Engineers
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• v.12 no.6
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• pp.48-59
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• 1990

A finite element program was developed using line elements for simulating the stretch/draw forming operation of an arbitrarily-shaped plane-strain section. An implicit, incremental, updated Lagrangian formulation is employed, introducing a minimum plastic work path assumption for each time step. Geometric and material nonlinearities are also considered within each time step. The finite element equation is based on the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The membrane approximation is adopted under the plane stress assumption. The sheet material is assumed to obey a rigid-viscoplastic constitutive law. The developed program was tested in the die-tryout of typical automotive inner panels. In order to determine a single friction coefficient and boundary length, FEM results and measurements of thinning for a stretched section of final die were compared. After finding analysis parameters, the sheet forming operations of original and final die designs were simulated. Excellent agreement between measured and computed thickness strains was obtained and the developed program was able to identify die designs which were rejected during die tryout.

• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.407-421
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• 2009

The present paper addresses the optimal design of composite laminates with the aim of minimizing free-edge delamination stresses. A technique involving the application of particle swarm optimization (PSO) integrated with FEM was developed for the optimization. Optimization was also conducted with the zero-order method (ZOM) included in ANSYS. The semi-analytical method, which provides an approximation of the interlaminar normal stress of laminates under in-plane load, was used to partially validate the optimization results. It was found that optimal results based on ZOM are sensitive to the starting design points, and an unsuitable initial design set will lead to a result far from global solution. By contrast, the proposed method can find the global optimal solution regardless of initial designs, and the solutions were better than those obtained by ZOM in all the cases investigated.