Search results for: Finite capacity

Authors: Reza Ziaie Moayed, Saeideh Mohammadi

Abstract:

Soft soil is used in many of civil engineering projects like coastal, marine and road projects. Because of low shear strength and stiffness of soft soils, large settlement and low bearing capacity will occur under superstructure loads. This will make the civil engineering activities more difficult and costlier. In the case of soft soils, improvement is a suitable method to increase the shear strength and stiffness for engineering purposes. In recent years, the artificial cementation of soil by cement and lime has been extensively used for soft soil improvement. Cement stabilization is a well-established technique for improving soft soils. Artificial cementation increases the shear strength and hardness of the natural soils. On the other hand, in soft soils, the use of piles to transfer loads to the depths of ground is usual. By using cement treated soil around the piles, high bearing capacity and low settlement in piles can be achieved. In the present study, lateral bearing capacity of short piles in cemented soils is investigated by numerical approach. For this purpose, three dimensional (3D) finite difference software, FLAC 3D is used. Cement treated soil has a strain hardening-softening behavior, because of breaking of bonds between cement agent and soil particle. To simulate such behavior, strain hardening-softening soil constitutive model is used for cement treated soft soil. Additionally, conventional elastic-plastic Mohr Coulomb constitutive model and linear elastic model are used for stress-strain behavior of natural soils and pile. To determine the parameters of constitutive models and also for verification of numerical model, the results of available triaxial laboratory tests on and insitu loading of piles in cement treated soft soil are used. Different parameters are considered in parametric study to determine the effective parameters on the bearing of the piles on cemented treated soils. In the present paper, the effect of various length and height of the artificial cemented area, different diameter and length of the pile and the properties of the materials are studied. Also, the effect of choosing a constitutive model for cemented treated soils in the bearing capacity of the pile is investigated.

Keywords: Cement-treated soils, pile, lateral capacity, FLAC 3D.

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Authors: M.Z. Islam, C.W. Lim

Abstract:

Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which governs the nonlocal material behavior. The new NL-FEM is adopted in such a way that the postulated nonlocal elastic behavior of material is captured by a finite element endowed with a set of (cross-stiffness) element itself by the other elements in mesh. An example with their analytical solutions and the relevant numerical findings for various load and boundary conditions are presented and discussed in details. It is observed from the numerical solutions that the torsional deformation angle decreases with increasing nonlocal nanoscale parameter. It is also noted that the analytical solution fails to capture the nonlocal effect in some cases where numerical solutions handle those situation effectively which prove the reliability and effectiveness of numerical techniques.

Keywords: NL-FEM, nonlocal elasticity, nanoscale, torsion.

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Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

Abstract:

Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: Decryption, encryption, elliptic curve, greater common divisor.

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Authors: H.Seidi, M.Jalali Azizpour, S.A.Zahedi

Abstract:

Today, Hydroforming technology provides an attractive alternative to conventional matched die forming, especially for cost-sensitive, lower volume production, and for parts with irregular contours. In this study the critical fluid pressures which lead to rupture in the workpiece has been investigated by theoretical and finite element methods. The axisymmetric analysis was developed to investigate the tearing phenomenon in cylindrical Hydroforming Deep Drawing (HDD). By use of obtained equations the effect of anisotropy, drawing ratio, sheet thickness and strain hardening exponent on tearing diagram were investigated.

Keywords: Hydroforming deep drawing, Pressure path, Axisymmetric analysis, Finite element simulation.

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Authors: Camille A. Issa, Omar Masri

Abstract:

In this study, the commercial finite element software ABAQUS was used to develop a three-dimensional nonlinear finite element model capable of simulating the pull-out test of reinforcing bars from underwater concrete. The results of thirty-two pull-out tests that have different parameters were implemented in the software to study the effect of the concrete cover, the bar size, the use of stirrups, and the compressive strength of concrete. The interaction properties used in the model provided accurate results in comparison with the experimental bond-slip results, thus the model has successfully simulated the pull-out test. The results of the finite element model are used to better understand and visualize the distribution of stresses in each component of the model, and to study the effect of the various parameters used in this study including the role of the stirrups in preventing the stress from reaching to the sides of the specimens.

Keywords: Bond strength, nonlinear finite element analysis, pull-out test, underwater concrete.

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Authors: Kasthurirangan Gopalakrishnan, Anshu Manik

Abstract:

Subgrade moisture content varies with environmental and soil conditions and has significant influence on pavement performance. Therefore, it is important to establish realistic estimates of expected subgrade moisture contents to account for the effects of this variable on predicted pavement performance during the design stage properly. The initial boundary soil suction profile for a given pavement is a critical factor in determining expected moisture variations in the subgrade for given pavement and climatic and soil conditions. Several numerical models have been developed for predicting water and solute transport in saturated and unsaturated subgrade soils. Soil hydraulic properties are required for quantitatively describing water and chemical transport processes in soils by the numerical models. The required hydraulic properties are hydraulic conductivity, water diffusivity, and specific water capacity. The objective of this paper was to determine isothermal moisture profiles in a soil fill and predict the soil moisture movement above the ground water table using a simple one-dimensional finite difference model.

Keywords: Fill, Hydraulic Conductivity, Pavement, Subgrade.

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Authors: Ali A. Al-Jazaairry, Tahsin T. Sabbagh

Abstract:

One of the important concerns within the field of geotechnical engineering is the presence of cavities in soils. This present work is an attempt to understand the behaviour of strip footing subjected to inclined load and constructed on cavitied soil. The failure mechanism of strip footing located above such soils was studied analytically. The capability of analytical model to correctly expect the system behaviour is assessed by carrying out verification analysis on available studies. The study was prepared by finite element software (PLAXIS) in which an elastic-perfectly plastic soil model was used. It was indicated, from the results of the study, that the load carrying capacity of foundation constructed on cavity can be analysed well using such analysis. The research covered many foundation cases, and in each foundation case, there occurs a critical depth under which the presence of cavities has shown minimum impact on the foundation performance. When cavities are found above this critical depth, the load carrying capacity of the foundation differs with many influences, such as the location and size of the cavity and footing depth. Figures involving the load carrying capacity with the affecting factors studied are presented. These figures offer information beneficial for the design of strip footings rested on underground cavities. Moreover, the results might be used to design a shallow foundation constructed on cavitied soil, whereas the obtained failure mechanisms may be employed to improve numerical solutions for this kind of problems.

Keywords: Axial load, cavity, inclined load, strip footing.

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation of winding numbers of paths of zeros of analytic theta functions. We have considered briefly an analytic representation of finite quantum systems ZN. The analytic functions on a torus have exactly N zeros. The brief introduction to the zeros of analytic functions and there time evolution is given. We have discussed the periodic finite quantum systems. We have introduced the winding numbers in general. We consider the winding numbers of the zeros of analytic theta functions.

Keywords: Winding numbers, period, paths of zeros.

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Authors: Trevor N. Haas, Alexander Koen

Abstract:

Columns have traditionally been constructed of reinforced concrete or structural steel. Much attention was allocated to estimate the axial capacity of the traditional column sections to the detriment of other forms of construction. Other forms of column construction such as Concrete Filled Double Skin Tubes received little research attention, and almost no attention when subjected to eccentric loading. This paper investigates the axial capacity of columns when subjected to eccentric loading. The experimental axial capacities are compared to other established theoretical formulae on concentric loading to determine a possible relationship. The study found a good correlation between the reduction in axial capacity for different column lengths and hollow section ratios.

Keywords: CSDST, CFST, Axial Capacity.

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Authors: Md Rashadul Islam, Mesbah U. Ahmed, Rafiqul A. Tarefder

Abstract:

This study evaluates the back calculation of stiffness of a pavement section on Interstate 40 (I-40)in New Mexico through numerical analysis. Falling Weight Deflectometer (FWD) test has been conducted on a section on I-40. Layer stiffness of the pavement has been backcalculated by a backcalculation software, ELMOD, using the FWD test data. Commercial finite element software, ABAQUS, has been used to develop the Finite Element Model (FEM) of this pavement section. Geometry and layer thickness are collected from field coring. Input parameters i.e. stiffnesses of different layers of the pavement are used as the backcalculated ones. Resulting surface deflections at different radial distances from the FEM analysis are compared with field FWD deflection values. It shows close agreement between the FEM and FWD outputs. Therefore, the FWD test method can be considered to be a reliable test procedure for evaluating the in situ stiffness of pavement material.

Keywords: Falling weight deflectometer test, Finite element model, Flexible pavement, moduli, surface deflection.

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Authors: Ahmet Tekcan

Abstract:

Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a.

Keywords: Singular curve, elliptic curve, rational points.

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Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

Abstract:

A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: Variational method, postbuckling, finite element method, intrinsic coordinate.

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Authors: R. O. Santos, L. P. Moreira, M. C. Cardoso

Abstract:

Spacer grid assembly supporting the nuclear fuel rods is an important concern in the design of structural components of a Pressurized Water Reactor (PWR). The spacer grid is composed by springs and dimples which are formed from a strip sheet by means of blanking and stamping processes. In this paper, the blanking process and tooling parameters are evaluated by means of a 2D plane-strain finite element model in order to evaluate the punch load and quality of the sheared edges of Inconel 718 strips used for nuclear spacer grids. A 3D finite element model is also proposed to predict the tooling loads resulting from the stamping process of a preformed Inconel 718 strip and to analyse the residual stress effects upon the spring and dimple design geometries of a nuclear spacer grid.

Keywords: Blanking process, damage model, finite element modelling, Inconel 718, spacer grids, stamping process.

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Authors: Won Mok. Choi, Tae Su. Kwon, Hyun Sung. Jung, Jin Sung. Kim

Abstract:

The aim of this paper is to confirm the effect of key design parameters, the punch radius and punch angle, on rupture of the expansion tube using a finite element analysis with a ductile damage model. The results of the finite element analysis indicated that the expansion ratio of the tube was mainly affected by the radius of the punch. However, the rupture was more affected by the punch angle than the radius of the punch. The existence of a specific punch angle, at which rupture did not occur, even if the radius of the punch was increased, was found.

Keywords: Expansion tube, Ductile damage, Shear failure, Stress triaxiality.

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Authors: Changsoo Chon, Sangkuy Han, Donghyun Seo, Jihyung Park, Bokku Kang, Hansung Kim, Keyoungjin Chun, Cheolwoong Ko

Abstract:

The purpose of the study is to develop a finite element model based on 3D bone structural images of Micro-CT and to analyze the stress distribution for the osteoporosis mouse femora. In this study, results of finite element analysis show that the early osteoporosis of mouse model decreased a bone density in trabecular region; however, the bone density in cortical region increased.

Keywords: Micro-CT, finite element analysis, osteoporosis, bone strength.

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Authors: M. M. Shokrieh, A. Karamnejad

Abstract:

This paper deals with a numerical analysis of the transient response of composite beams with strain rate dependent mechanical properties by use of a finite difference method. The equations of motion based on Timoshenko beam theory are derived. The geometric nonlinearity effects are taken into account with von Kármán large deflection theory. The finite difference method in conjunction with Newmark average acceleration method is applied to solve the differential equations. A modified progressive damage model which accounts for strain rate effects is developed based on the material property degradation rules and modified Hashin-type failure criteria and added to the finite difference model. The components of the model are implemented into a computer code in Mathematica 6. Glass/epoxy laminated composite beams with constant and strain rate dependent mechanical properties under dynamic load are analyzed. Effects of strain rate on dynamic response of the beam for various stacking sequences, load and boundary conditions are investigated.

Keywords: Composite beam, Finite difference method, Progressive damage modeling, Strain rate.

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Authors: Abdolamir Nekoubin

Abstract:

One of Effective parameters on the performance of linear induction motors is number of poles which must be selected and optimized to increase power efficiency and motor performance significantly. In this paper a double-sided linear induction motor with different poles number by using MAXWELL3D software is designed and with finite element method is analyzed electromagnetically. Then for dynamic simulation, linear motor by using MATLAB software is simulated. The results show that by adding poles number, system time response is increased and motor after more time reaches to steady state. Also propulsion force of motor is increased.

Keywords: Linear motor, poles number, finite element method.

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Authors: Rachelle Bosua, Nina Evans

Abstract:

The resource-based view of the firm regards knowledge as one of the most important organizational assets and a key strategic resource that contributes unique value to organizations. The acquisition, absorption and internalization of external knowledge are central to an organization-s innovative capabilities. This ability to evaluate, acquire and integrate new knowledge from its environment is referred to as a firm-s absorptive capacity (AC). This research in progress paper explores the link between interorganizational Social Networks (SNs) and a firm-s Absorptive Capacity (AC). Based on an in-depth literature survey of both concepts, four propositions are proposed that explain the link between AC and SNs. These propositions suggest that SNs are key to a firm-s AC. A qualitative research method is proposed to test the set of propositions in the next stage of this research.

Keywords: Knowledge, Innovation, Absorptive Capacity, Social Networks

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Authors: M. Pala Prasad Reddy, Jeevamma Jacob

Abstract:

Accurate dynamic modeling and analysis of flexible link manipulator (FLM) with non linear dynamics is very difficult due to distributed link flexibility and few studies have been conducted based on assumed modes method (AMM) and finite element models. In this paper a nonlinear dynamic model with first two elastic modes is derived using combined Euler/Lagrange and AMM approaches. Significant dynamics associated with the system such as hub inertia, payload, structural damping, friction at joints, combined link and joint flexibility are incorporated to obtain the complete and accurate dynamic model. The response of the FLM to the applied bang-bang torque input is compared against the models derived from LS-DYNA finite element discretization approach and linear finite element models. Dynamic analysis is conducted using LS-DYNA finite element model which uses the explicit time integration scheme to simulate the system. Parametric study is conducted to show the impact payload mass. A numerical result shows that the LS-DYNA model gives the smooth hub-angle profile.

 

Keywords: Flexible link manipulator, AMM, FEM, LS-DYNA, Bang-bang torque input.

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Authors: Siminfar Samakoush Galougah

Abstract:

In this paper, we study two power allocation problems for an uplink user-centric (UC) cell-free massive multiple-input multiple-output (CF-mMIMO) system. Besides, we assume each access point (AP) is connected to a central processing unit (CPU) via fronthaul link with limited capacity. To efficiently use the fronthaul capacity, two strategies for transmitting signals from APs to the CPU are employed; namely: compress-forward-estimate (CFE), estimate-compress-forward (ECF). The capacity of the aforementioned strategies in user-centric CF-mMIMO are drived. Then, we solved the two power allocation problems with minimum Spectral Efficiency (SE) and sum-SE maximization objectives for ECF and CFE strategies.

Keywords: Cell-free massive MIMO, limited capacity fronthaul, spectral efficiency, power allocation problem.

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Authors: P. Meesuk, T. Kulworawanichpong, P. Pao-la-or

Abstract:

This paper proposes a set of quasi-static mathematical model of magnetic fields caused by high voltage conductors of distribution transformer by using a set of second-order partial differential equation. The modification for complex magnetic field analysis and time-harmonic simulation are also utilized. In this research, transformers were study in both balanced and unbalanced loading conditions. Computer-based simulation utilizing the threedimensional finite element method (3-D FEM) is exploited as a tool for visualizing magnetic fields distribution volume a distribution transformer. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. At present, the FEM has been widely applied in most engineering fields. Even for problems of magnetic field distribution, the FEM is able to estimate solutions of Maxwell-s equations governing the power transmission systems. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Distribution Transformer, Magnetic Field, Load Unbalance, 3-D Finite Element Method (3-D FEM)

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Authors: R. K. Apalowo, D. Chronopoulos, V. Thierry

Abstract:

A wave finite element (WFE) and finite element (FE) based computational method is presented by which the dispersion properties as well as the wave interaction coefficients for one-dimensional structural system can be predicted. The structural system is discretized as a system comprising a number of waveguides connected by a coupling joint. Uniform nodes are ensured at the interfaces of the coupling element with each waveguide. Then, equilibrium and continuity conditions are enforced at the interfaces. Wave propagation properties of each waveguide are calculated using the WFE method and the coupling element is modelled using the FE method. The scattering of waves through the coupling element, on which damage is modelled, is determined by coupling the FE and WFE models. Furthermore, the central aim is to evaluate the effect of pressurization on the wave dispersion and scattering characteristics of the prestressed structural system compared to that which is not prestressed. Numerical case studies are exhibited for two waveguides coupled through a coupling joint.

Keywords: Finite element, prestressed structures, wave finite element, wave propagation properties, wave scattering coefficients.

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Authors: Dongheon Shin, Kyungnam Ko, Jongchul Huh

Abstract:

The investigation on wind turbine degradation was carried out using the nacelle wind data. The three Vestas V80-2MW wind turbines of Sungsan wind farm in Jeju Island, South Korea were selected for this work. The SCADA data of the wind farm for five years were analyzed to draw power curve of the turbines. It is assumed that the wind distribution is the Rayleigh distribution to calculate the normalized capacity factor based on the drawn power curve of the three wind turbines for each year. The result showed that the reduction of power output from the three wind turbines occurred every year and the normalized capacity factor decreased to 0.12%/year on average.

Keywords: Wind energy, Power curve, Capacity factor, Annual energy production.

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Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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Authors: Satish BM, Girish BM , Mahesh K

Abstract:

The aim of the present work is to study the effect of annealing on the vibration damping capacity of high-chromium (16%) ferromagnetic steel. The alloys were prepared from raw materials of 99.9% purity melted in a high frequency induction furnace under high vacuum. The samples were heat-treated in vacuum at various temperatures (800 to 1200ºC) for 1 hour followed by slow cooling (120ºC/h). The inverted torsional pendulum method was used to evaluate the vibration damping capacity. The results indicated that the vibration damping capacity of the alloys is influenced by annealing and there exists a critical annealing temperature after 1000ºC. The damping capacity increases quickly below the critical temperature since the magnetic domains move more easily.

Keywords: Vibration, Damping, Ferromagnetic, Steel.

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Authors: A.Roshandel, N.Hedayat, H.kiamanesh

Abstract:

Today, numerical simulation is a powerful tool to solve various hydraulic engineering problems. The aim of this research is numerical solutions of shallow water equations using finite volume method for Simulations of dam break over wet and dry bed. In order to solve Riemann problem, Roe-s approximate solver is used. To evaluate numerical model, simulation was done in 1D and 2D states. In 1D state, two dam break test over dry bed (with and without friction) were studied. The results showed that Structural failure around the dam and damage to the downstream constructions in bed without friction is more than friction bed. In 2D state, two tests for wet and dry beds were done. Generally in wet bed case, waves are propagated to canal sides but in dry bed it is not significant. Therefore, damage to the storage facilities and agricultural lands in wet bed case is more than in dry bed.

Keywords: dam break, dry bed, finite volume method, shallow water equations.

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Authors: Nicola Gualandi, Luca Mantecchini, Davide Serrau

Abstract:

Airport capacity has always been perceived in the traditional sense as the number of aircraft operations during a specified time corresponding to a tolerable level of average delay and it mostly depends on the airside characteristics, on the fleet mix variability and on the ATM. The adoption of the Directive 2002/30/EC in the EU countries drives the stakeholders to conceive airport capacity in a different way though. Airport capacity in this sense is fundamentally driven by environmental criteria, and since acoustical externalities represent the most important factors, those are the ones that could pose a serious threat to the growth of airports and to aviation market itself in the short-medium term. The importance of the regional airports in the deregulated market grew fast during the last decade since they represent spokes for network carriers and a preferential destination for low-fares carriers. Not only regional airports have witnessed a fast and unexpected growth in traffic but also a fast growth in the complaints for the nuisance by the people living near those airports. In this paper the results of a study conducted in cooperation with the airport of Bologna G. Marconi are presented in order to investigate airport acoustical capacity as a defacto constraint of airport growth.

Keywords: Airport acoustical capacity, airport noise, air traffic noise, sustainability of regional airports.

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Authors: Seyed Abolhasan Naeini, M. Mortezaee

Abstract:

Various factors such as the method of installation, the pile type, the pile material and the pile shape, can affect the final bearing capacity of a pile executed in the soil; among them, the method of installation is of special importance. The physical modeling is among the best options in the laboratory study of the piles behavior. Therefore, the current paper first presents and reviews the frustum confining vessel (FCV) as a suitable tool for physical modeling of deep foundations. Then, by describing the loading tests of two open-ended and closed-end steel piles, each of which has been performed in two methods, “with displacement" and "without displacement", the effect of end conditions and installation method on the final bearing capacity of the pile is investigated. The soil used in the current paper is silty sand of Firuzkuh, Iran. The results of the experiments show that in general the without displacement installation method has a larger bearing capacity in both piles, and in a specific method of installation the closed ended pile shows a slightly higher bearing capacity.

Keywords: physical modeling, frustum confining vessel, pile, bearing capacity, installation method

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Authors: Hyung-Jin Jang, Kwang-Bok Shin, Sung-Ho Han

Abstract:

This paper describes the crashworthiness assessment and improvement of tlting train made of sandwich composites. The crashworhiness assessment of tilting train was conducted according to four collision scenarios of the Korean railway safety law. Collision analysis was carried out using explicit finite element analysis code LS-DYNA 3D. The finite element model consists of 3-D finite element model and 1-D equivalent model to save the finite element modeling and calculation time. It found that the crashworthiness analysis results were satisfied with the performance requirements except the crash scenario-2. In order to meet the crashworthiness requirements for crash scenario-2, the stiffness reinforcement for the laminate composite cover and metal frames of cabmask structure were proposed. Consequentially, it has satisfied the requirement for crash scenario-2.

Keywords: Crashworthiness, collision scenario, Korean railway safety law, sandwich composite, tilting train.

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Authors: B. S. Jayashankarbabu, Karisiddappa

Abstract:

The finite element method is used to obtain the elastic buckling load factor for square isotropic plate containing circular, square and rectangular cutouts. ANSYS commercial finite element software had been used in the study. The applied inplane loads considered are uniaxial and biaxial compressions. In all the cases the load is distributed uniformly along the plate outer edges. The effects of the size and shape of concentric cutouts with different plate thickness ratios and the influence of plate edge conditions, such as SSSS, CCCC and mixed boundary condition SCSC on the plate buckling strength have been considered in the analysis.

Keywords: Concentric cutout, Elastic buckling, Finite element method, Inplane loads, Thickness ratio.

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