• Structural Engineering and Mechanics
• /
• v.10 no.1
• /
• pp.67-79
• /
• 2000

Critical loads and load-carrying capacities for steel scaffolds used as shoring systems were compared using computational and experimental methods in Part I of this paper. In that paper, a simple 2-D model was established for use in evaluating the structural behavior of scaffold-shoring systems. This 2-D model was derived using an incremental finite element analysis (FEA) of a typical complete scaffold-shoring system. Although the simplified model is only two-dimensional, it predicts the critical loads and failure modes of the complete system. The objective of this paper is to present a closed-form solution to the 2-D model. To simplify the analysis, a simpler model was first established to replace the 2-D model. Then, a closed-form solution for the critical loads and failure modes based on this simplified model were derived using a bifurcation (eigenvalue) approach to the elastic-buckling problem. In this closed-form equation, the critical loads are shown to be function of the number of stories, material properties, and section properties of the scaffolds. The critical loads and failure modes obtained from the analytical (closed-form) solution were compared with the results from the 2-D model. The comparisons show that the critical loads from the analytical solution (simplified model) closely match the results from the more complex model, and that the predicted failure modes are nearly identical.

• Structural Engineering and Mechanics
• /
• v.38 no.2
• /
• pp.157-169
• /
• 2011

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

• Computers and Concrete
• /
• v.23 no.1
• /
• pp.11-23
• /
• 2019

Nowadays, the characterization of Ultra-High Performance Fiber-Reinforced Concrete (UHPFRC) tensile behavior still remains a challenge for researchers. For this purpose, a simplified closed-form non-linear hinge model based on the Third Point Bending Test (ThirdPBT) was developed by the authors. This model has been used as the basis of a simplified inverse analysis methodology to derive the tensile material properties from load-deflection response obtained from ThirdPBT experimental tests. In this paper, a non-linear finite element model (FEM) is presented with the objective of validate the closed-form non-linear hinge model. The state determination of the closed-form model is straightforward, which facilitates further inverse analysis methodologies to derive the tensile properties of UHPFRC. The accuracy of the closed-form non-linear hinge model is validated by a robust non-linear FEM analysis and a set of 15 Third-Point Bending tests with variable depths and a constant slenderness ratio of 4.5. The numerical validation shows excellent results in terms of load-deflection response, bending curvatures and average longitudinal strains when resorting to the discrete crack approach.

• Structural Engineering and Mechanics
• /
• v.20 no.1
• /
• pp.45-67
• /
• 2005

This paper presents a new approach to predict the racking load-displacement response of plasterboard clad walls found in Australian light-framed residential structures under monotonic racking load. The method is based on a closed-form mathematical model, described herein as the 'Modularised' Closed-Form Mathematical model or MCFM model. The model considers the non-linear behaviour of the connections between the plasterboard cladding and frame. Furthermore, the model is flexible as it enables incorporation of different nailing patterns for the cladding. Another feature of this model is that the shape of stud deformation is not assumed to be a specific function, but it is computed based on the strain energy approach to take account of the actual load deformation characteristics of particular walls. Verification of the model against the results obtained from a detailed Finite Element (FE) model is also reported. Very good agreement between the closed form solution and that of the FE model was achieved.

• Advances in aircraft and spacecraft science
• /
• v.8 no.4
• /
• pp.273-287
• /
• 2021

Model-based, data-driven and physics-based approaches represent the state-of-the-art techniques to estimate the aircraft flow angles, angle-of-attack and angle-of-sideslip, in avionics. Thanks to sensor fusion techniques, a synthetic sensor is able to provide estimation of flow angles without any dedicated physical sensors. The work deals with a physics-based scheme derived from flight mechanic theory that leads to a nonlinear flow angle model. Even though several solvers can be adopted, nonlinear models can be replaced with less accurate but straightforward ones in practical applications. The present work proposes a linearisation to obtain the flow angles' closed form solution that is verified using a flight simulator. The main objective of the paper, in fact, is to analyse the estimation degradation using the proposed closed form solutions with respect to the nonlinear scheme. Moreover, flight conditions, where the proposed closed form solutions are not applicable, are identified.

• Communications of the Korean Mathematical Society
• /
• v.29 no.3
• /
• pp.489-496
• /
• 2014

We drive a closed-form expression for the price of a European quanto call option in the double square root stochastic volatility model.

• Communications of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.415-422
• /
• 2016

We derive a closed-form expression for the price of a European quanto call option when both foreign and domestic interest rates follow the Vasicek's short rate model.

• Structural Engineering and Mechanics
• /
• v.81 no.1
• /
• pp.39-50
• /
• 2022

Layer separation (delamination) is an essential threat to fiber-reinforced polymer (FRP) plates under dynamic, static, and fatigue loads. Under compressive load, the growth of delamination will lead to structural instability. The aim of this paper is to present a method using shape memory alloy (SMA) stitches to suppress the delamination growth in a FRP plate and to improve the buckling behavior of the plate with a rectangular hole. The present paper is divided into two parts. Firstly, a closed-form (CF) formulation for evaluating the buckling load of the FRP plate is presented. Secondly, the finite element method (FEM) will be employed to calculate the buckling loads of the plates which serves to validate the results obtained from the closed-form method. The novelty of this work is the development of the closed-form solution using the p-Ritz energy approach regarding the stress-dependent phase transformation of SMA to trace the equilibrium path. For the FEM, the Lagoudas constitutive model of the SMA material is implemented in FORTRAN programming language using a user material subroutines (VUMAT). The model is simulated in ABAQUS/Explicit solver due to the nature of the loading type. The cohesive zone model (CZM) is applied to simulate the delamination growth.

• Journal of Korea Society of Industrial Information Systems
• /
• v.19 no.3
• /
• pp.75-85
• /
• 2014

This paper is to develop and estimate a closed form inflation model using the estimates for real marginal costs in manufacturing industries during the sample period 1975-2010. The production function in manufacturing industry incorporates labor, capital, domestic material, and foreign material, assuming constant returns to scale technology and AR(1) process of technological coefficient. We derive real marginal costs from firm's cost minimization with quarterly data and provide new evidences on the new Keynesian Phillips curve for Korea. The main empirical result is that the closed form coefficients ${\delta}_1$ and ${\delta}^{-1}_2$ in manufacturing for PPI inflation proved to be 0.5086 and 0.8779 respectively, similar to the estimates in the U.S. case. These results also are consistent with the functional relationship between the coefficients in hybrid model and its closed form. Thus the paper suggests that the empirical studies on inflation dynamics need to focus on the manufacturing industry with market power, treating PPI inflation as the dependent variable.

• Structural Engineering and Mechanics
• /
• v.14 no.3
• /
• pp.345-364
• /
• 2002

The scaling laws for vibration response of anti-symmetrically laminated plates are derived by applying the similitude transformation to the governing differential equations directly. With this approach, a closed-form solution of the governing equations is not required. This is a significant advantage over the method employed by other researchers where similitude transformation is applied to the closed-form solution. The scaling laws are tested by comparing the similitude fundamental frequencies to the theoretical fundamental frequencies determined from the available closed-form solutions. In case of complete similitude, similitude solutions from the scaling laws exactly agree with the theoretical solutions. Sometimes, it may not be feasible to select the model which obeys the similarity requirement completely, therefore partial similitude is theoretically investigated and approximate scaling laws are recommended. The distorted models in stacking sequences and laminated material properties demonstrate reasonable accuracy. On the contrary, a model with distortion in fiber angle is not recommended. The derived scaling laws are very useful to determine the vibration response of complex prototypes by performing the experiment on a model with required similarities.