• Journal of Korean Association for Spatial Structures
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• v.2 no.1 s.3
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• pp.75-84
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• 2002

In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.203-216
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• 1999

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.43-68
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• 2007

Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.3
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• pp.169-176
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• 1998

A method for the dynamic analysis of multibody systems undertaking impulsive force is introduced in this paper. A partial velocity matrix based on Kane's method is introduced to reduce the number of equations to be solved. Only minimum number of equations of motion can be obtained by using the partial velocity matrix. This reduces the computational effort significantly to obtain the dynamic response of the system. At the very moment of the impulse, instead of using the numerical integrator to solve the equations of motion, the impulse and momentum principle is used to obtain the dynamic response. The impulse as wall as the reaction force acting on the kinematic joints can easily calculated too.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.973-992
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• 2016

A direct and relatively simple method for controlling nodal displacements and/or internal bar forces has been developed for prestressable structural assemblies including complex elements ("macro-elements", e.g., the pantographic element), involving Matrix Condensation, in which structural matrices being built up from matrices of elementary elements. The method is aimed at static shape control of geometrically sensitive structures. The paper discusses identification of the most effective bars for actuation, without incurring violation in bar forces, and also with objective of minimal number of actuators or minimum actuation. The advantages of the method is that the changes for both force and displacement regimes are within a single formulation. The method can also be used for adjustment of bar forces to either reduce instances of high forces or increase low forces (e.g., in a cable nearing slack).

• 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.30 no.4
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• pp.387-402
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• 2008

The Integrated Force Method (IFM) has been developed in recent years for the analysis of civil, mechanical and aerospace engineering structures. In this method all independent or internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. The solution by IFM needs the computation of element equilibrium and flexibility matrices from the assumed displacement, stress-resultant fields and material properties. This paper presents a general purpose code for the automatic generation of element equilibrium and flexibility matrices for plate bending elements using the Integrated Force Method. Kirchhoff and the Mindlin-Reissner plate theories have been employed in the code. Paper illustrates development of element equilibrium and flexibility matrices for the Mindlin-Reissner theory based four node quadrilateral plate bending element using the Integrated Force Method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.6
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• pp.807-813
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• 1986

The orthogonal cutting method of the nodular graphite cast iron in the lathe turning, whose matrix were formulated under two kinds of annealing conditions, has been experimentally studied and the results investigated. The various characteristics of machinabilities of the nodular cast iron, depending upon its matrix, have been obtained from the results as follows. (1) As depth of cut increases, the cutting ratio and the shear angles tend to slightly increase, and as the containing quantity of ferrite matrix increases, they slightly decrease. (2) As depth of cut increases, the cutting force increases in an approximate straight line, and as the containing quantity of ferrite matrix increases, they decreases and the decreasing rate is about 20-30%. (3) As the containing quantity of ferrite matrix increases, the friction force acting on the tool face decreases and the decreasing rate is about 34-40% in case of the lower depth of cut, but in case of the higher depth of cut the decreasing rate is very small. (4) Both shearing force and vertical force show a lineal increases, and according as ferrite matrix increases there is a decrease by 25% in shearing force and a 12-25% decrease in vertical force. (5) Shearing speed and chip flow speed keep almost a constant value irrespective of matrix.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.8
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• pp.79-86
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• 2001

A method for actively minimizing dynamic reaction forces in a flexible structure subject to persistent excitations is presented. One difficulty with the method, however, is that forces and moments do not converge as quickly as displacements in mathematical discretization of continuous systems, so a controller based on a truncated model of a continuous system can produce poor results. A technique using residual flexibility matrix is presented for correcting the truncated force representation. A controller designed for reaction force minimization, using the residual flexibility matrix, is applied to a model of a flexible structure, and the results are presented. Implications of various reaction force penalty combinations on the resulting control performance are also discussed.

• Structural Engineering and Mechanics
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• v.29 no.6
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• pp.659-671
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• 2008

A procedure to analyse the space frame structure fixed at base as well as resting on sliding bearing using total or absolute displacement in dynamic equation is developed. In the present method, the effect of ground acceleration is not considered as equivalent force. Instead, the ground acceleration is considered as a known value in the acceleration vector at degree of freedom corresponding to base of the structure when the structure is in non-sliding phase. When the structure is in sliding phase, only a force equal to the maximum frictional resistance is applied at base. Also, in this method, the stiffness matrix, mass matrix and the damping matrix will not change when the structure enters from one phase to another. The results obtained from the present method using absolute displacement approach are compared with the results obtained from the analysis of structure using relative displacement approach. The applicability of the analysis is also demonstrated to obtain the response of the structure resting on sliding bearing with restoring force device.