• Bulletin of the Society of Naval Architects of Korea
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• v.14 no.1
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• pp.11-17
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• 1977

In order to design safer and more economical ship structures, theoretical structure analysis of entire vessel is desirable. This paper describes the application of the Direct Stiffness Method to ship structures for calculation of forces and moments which act on each part of ship structures. Before application of this method, ship structures have to be replaced with equivalent space frame. Emphasis is placed on the division of total stiffness matrix of entire vessel. Floating barge, of which principal dimensions are $L{\times}B{\times}D=16M{\times}10M{\times}2M$, is taken as calculation sample. The conclusion of this paper is that, in initial stage of ship structure design, the Direct Stiffness Method by Division can be applied to determine frame-space and scantlings of members.

• Steel and Composite Structures
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• v.21 no.1
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• pp.195-216
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• 2016

The dynamic characteristics of continuous steel-concrete composite beams considering the effect of interlayer slip were investigated based on Euler Bernoulli's beam theory. A simplified calculation model was presented, in which the Mode Stiffness Matrix (MSM) was developed. The natural frequencies and modes of partial-interaction composite continuous beams can be calculated accurately and easily by the use of MSM. Proceeding from the present method, the natural frequencies of two-span steel-concrete composite continuous beams with different span-ratios (0.53, 0.73, 0.85, 1) and different shear connection stiffnesses on the interface are calculated. The influence pattern of interfacial stiffness on bending vibration frequency was found. With the decrease of shear connection stiffness on the interface, the flexural vibration frequencies decrease obviously. And the influence on low order modes is more obvious while the reduction degree of high order is more sizeable. The real natural frequencies of partial-interaction continuous beams commonly used could have a 20% to 40% reduction compared with the fully-interaction ones. Furthermore, the reduction-ratios of natural frequencies for different span-ratios two-span composite beams with uniform shear connection stiffnesses are totally the same. The span-ratio mainly impacts on the mode shape. Four kinds of shear connection stiffnesses of steel-concrete composite continuous beams are calculated and compared with the experimental data and the FEM results. The calculated results using the proposed method agree well with the experimental and FEM ones on the low order modes which mainly determine the vibration properties.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.487-501
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• 2023

Nanoparticles have lower size and larger specific surface area, good stability and less toxic and side effects. In recent years, with the development of nanotechnology, its application range has become wider and wider, especially in the field of biomedicine, which has received more and more attention. Bone defect repair materials with high strength, high elasticity and high tissue affinity can be prepared by nanotechnology. The purpose of this paper was to study how to analyze and study the composite materials for sports bone injury based on multifunctional nanomaterials, and described the electrospinning method. In this paper, nano-sized zirconia (ZrO₂) filled micro-sized hydroxyapatite (HAP) composites were prepared according to the mechanical properties of bone substitute materials in the process of human rehabilitation. Through material tensile and compression experiments, the performance parameters of ZrO₂/HAP composites with different mass fraction ratios were analyzed, the influence of filling ZrO₂ particles on the mechanical properties of HAP matrix materials was clarified, and the effect of ZrO₂ mass fraction on the mechanical properties of matrix materials was analyzed. From the analysis of the compressive elastic modulus, when the mass fraction of ZrO₂ was 15%, the compressive elastic modulus of the material was 1222 MPa, and when 45% was 1672 MPa. From the analysis of compression ratio stiffness, when the mass fraction of ZrO₂ was 15%, the compression ratio stiffness was 658.07 MPa·cm³/g, and when it was 45%, the compression ratio stiffness is 943.51MPa·cm³/g. It can be seen that by increasing the mass fraction of ZrO₂, the stiffness of the composite material can be effectively increased, and the ability of the material to resist deformation would be increased. Typically, the more stressed the bone substitute material, the greater the stiffness of the compression ratio. Different mass fractions of ZrO₂/HAP filling materials can be selected to meet the mechanical performance requirements of sports bone injury, and it can also provide a reference for the selection of bone substitute materials for different patients.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.5
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• pp.1130-1139
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• 2001

Springs are widely utilized in machine element. To find out stiffness of coil spring, the space beam theory using the finite element method is adopted in this paper. In three dimensional space, a space frame element is a straight bar of uniform cross section which is capable of resisting axial forces, bending moments about two principal axes in the plane of its cross section and twisting moment about its centroidal axis. The corresponding displacement degrees of freedom are twelve. The displacements of nodal points due to small increment of force are calculated by the finite element method and the calculated nodal displacements are added to coordinates of nodal points. The new stiffness matrix of the system using the new coordinates of nodal points is adopted to calculated the another increments of nodal displacements, that is, the step by step method is used in this paper. The results of the finite element method are fairly well agreed with those of various experiments. Using MATLAB program developed in this paper, spring constants can be predicted by input of few factors.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.35 no.9
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• pp.159-169
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• 2019

This work presents the three-dimensional extended strain smoothing approach in the framework of finite element method, so-called smoothed finite element method (S-FEM) for quasi-incompressible hyperelastic materials undergoing the large deformations. The proposed method is known that the incompressible limits, such as over-estimation of stiffness and distorted mesh sensitivity, can be overcome in two dimensions. Therefore, in this paper, the idea of Cell-based, Edge-based and Node-based strain smoothing approaches is extended to three-dimensions. The construction of subcells and smoothing domains for each methods are explained. The smoothed strain-displacement matrix and the stiffness matrix are obtained on each smoothing domain in the same manner with two-dimensional S-FEM. Various numerical tests are studied to demonstrate the validity and accuracy of 3D-S-FEM. The obtained results are compared with analytical solutions to express the efficacy of the methods.

• Composites Research
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• v.16 no.1
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• pp.42-49
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• 2003

Brittle matrix composites often have interfacial debonding between the fiber and matrix which may lead to strength and stiffness degradation. The effect of interfacial debonding and fiber volume fraction on the mechanical properties of composite material were studied by using finite element method. Firstly, the modelling of fiber and matrix constituting the composite material was simplified under some assumptions. Traction and displacement continuity conditions were imposed along the boundary of adjacent representative volume elements. In order to obtain the effective material properties of composite material, stiffness constants were inverted. Numerical values of longitudinal moduli in case of perfect bonding were compared with theoretical values obtained by rule of mixtures and yielded consistency. Material properties of composite with large debonding an81e were found to decrease even though the fiber volume fraction increased.

• Journal of the Korean Society of Safety
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• v.7 no.2
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• pp.30-41
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• 1992

Analysis of Dynamic Characterisocs of Rectangular Plate by Finite Element Method. Dynamic characteristics of a rectangular plate with opening in it is studied by finite element method. To investigate these characteristics 12 degrees of freedom membrane finite element in used. The rectangular membrane finite elements are defined by specifying geometry, internal displacement functions and strain-displacement relations. Then, the governing equation for the finite element is derived by energy method. To derive the mass matrix and stiffness matrix of the element, expressions for strain and kineic energy in terms of the node displacement are generated. In constructing the overall structure matrix, the matrix of each elements are superposed and partitioned by applying the given boundary condition to obtain a nonslngular matrix. To find the natural freguencies and viration modes, the eigen values and the corresponding eigen vectors are computed by the computer using well known Jacobi power method. In order to verify the capability of the membrane finite element, a flat rectangular plate is analyzed first, and the result is compared with well known analytical results to show the good agreement. A rectangular plate with opening in It is analyzed with the same finite element. The results are presented in this paper. Unfortunately, the literature study could not provide with some results to compare, but the results reveal that the output of this research is phlslcally reasonable. And the results of this research are useful not only in practice but also for the future experimental research in comparison purpose.

• Structural Engineering and Mechanics
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• v.37 no.6
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• pp.633-648
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• 2011

This paper investigates the aspect-ratio locking of the isoparametric 8-node quadrilateral (QUAD8) element. An important finding is that, if finite element solution is carried out with in exact arithmetic (i.e., with no truncation and round off errors), the locking tendency of the element is completely avoided even for aspect-ratios as high as 100000. The current finite element codes mostly use floating point arithmetic. Thus, they can only avoid this locking for aspect-ratios up to 100 or 1000. A novel method is proposed in the paper to avoid aspect-ratio locking in floating point computations. In this method, the offending terms of the strain-displacement matrix (i.e., $\mathbf{B}$-matrix) are multiplied by suitable scaling factors to avoid ill-conditioning of stiffness matrix. Numerical examples are presented to demonstrate the efficacy of the method. The examples reveal that aspect-ratio locking is avoided even for aspect-ratios as high as 100000.

• Earthquakes and Structures
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• v.3 no.3_4
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• pp.383-411
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• 2012

The objective of the present paper is to review and implement the most recent developments in the Spectral Element Method (SEM), as well as improve aspects of its implementation in the study of wave propagation by numerical simulation in elastic unbounded domains. The classical formulation of the method is reviewed, and the construction of the mass matrix, stiffness matrix and the external force vector is expressed in terms of matrix operations that are familiar to earthquake engineers. To account for the radiation condition at the external boundaries of the domain, a new absorbing boundary condition, based on the Perfectly Matched Layer (PML) is proposed and implemented. The new formulation, referred to as the Multi-Axial Perfectly Matched Layer (M-PML), results from generalizing the classical Perfectly Matched Layer to a medium in which damping profiles are specified in more than one direction.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.113-125
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• 2007

Improved numerical method to obtain the exact stiffness matrices is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric and open/closed thin-walled beam on elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column This numerical technique is accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Next polynomial expressions as trial solutions are assumed for displacement parameters corresponding to zero eigenvalues and the eigenmodes containing undetermined parameters equal to the number of zero eigenvalues are determined by invoking the identity condition. And then the exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions. In order to illustrate the accuracy and the practical usefulness of this study, the numerical solutions are compared with results obtained from the thin-walled beam and shell elements.