• Transactions of the Korean Society of Automotive Engineers
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• v.24 no.2
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• pp.205-213
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• 2016

Heat loss and fin efficiency of symmetric and asymmetric trapezoidal fins with variable slope of fin's top surface are obtained by using a two-dimensional analytic method. Shapes of symmetric and asymmetric fins are changed from rectangular through trapezoidal to triangular by adjusting the fin shape factor. The ratio of symmetric trapezoidal fin length to asymmetric trapezoidal fin length is presented as a function of fin base height and convection characteristic number. The ratio of symmetric trapezoidal fin efficiency to asymmetric trapezoidal fin efficiency is presented as a function of the fin base height and fin shape factor. One of results shows that asymmetric trapezoidal fin length is shorter than symmetric trapezoidal fin length (i.e., asymmetric trapezoidal fin volume is smaller than symmetric trapezoidal fin volume) for the same heat loss when the fin base height and fin shape factor are the same.

• Magazine of the Korean Society of Agricultural Engineers
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• v.19 no.4
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• pp.4533-4543
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• 1977

The purpose of this study was to investigate and compare flow discharges of rectangular, V-notch and trapezoidal type of cutthrooat flumes, and the published data for trapezoidal parshall flumes. And the trapezoidal cutthroat flumes were also compared in their accuracy of discharge measurements for various convergence ratios in the inlet section and divergence ratios in the outlet section. Five flumes were studied, and all the flumes were 45cm long with flat-bottom and were made of well-finished transparent acryl plate of 3mm thickness. One rectangular, one V-notch and three trapezoidal types were numbered 1 to 5 as shown in Fig. III-1. The measured depth of water was ranged from 5 to 20cm. The results obtained in this study are summarized as follows: 1. The general discharge equations for tested prototypes are listed for free flow in Table IV-1 and for submergence flow in Table IV-4. 2. In both free and submerged flow, the accuracy of the discharge formula obtained by this test is highly significant at 1% level as shown in Table IV-2 and Table IV-6. The accuracy of disharges measured depends upon the convergence and divergence ratios in the trapezoidal types: the less the ratios of convergence as well as divergence, the lower the accuracy. 3. Submergence ratios tend to increase in the order of flume number except flume No. 4. This implies that trapezoidal cutthroat flumes are more acceptable than rectangular or V-notch ones for free flow. 4. The transition submergence for the trapezoidal Parshall flumes ranges from 80-85 percent, which is slightly higher than the tested flume. However, the trapezoidal cutthroat flume No. 5 has higher transition submergence ratio, ranging from 73-78 percent, than other trapezoidal ones. The difference between the trapezoidal Parshall flumes and the trapezoidal cutthroat flumes in transition submergence seems small enough to be ignored in their field use. 5. Trapezoidal cutthroat flume is simple and economical to construct in existing openchannels whose shapes are generally trapezoidal. In order to obtain the best rating accuracy, flume No. 3 among the tested trapezoidal types is recommended, because it shows the highest accuracy for both free and submerged flow.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.253-266
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• 2011

We would like to generalize about trapezoidal fuzzy set and to calculate four operations based on the Zadeh's extension principle for two generalized trapezoidal fuzzy sets. And we roll up triangular fuzzy numbers and generalized triangular fuzzy sets into it. Since triangular fuzzy numbers and generalized triangular fuzzy sets are generalized trapezoidal fuzzy sets, we need no more the separate painstaking calculations of addition, subtraction, multiplication and division for two such kinds once the operations are done for generalized trapezoidal fuzzy sets.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.291-303
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• 2014

In this paper, through a direct computation with subintervals partitioning [0, 1], we compute better a posteriori bounds for the average case error of the difference between the true value of $I(f)=\int_{0}^{1}f(x)dx$ with $f{\in}C^r$[0, 1] minus the composite trapezoidal rule and the composite trapezoidal rule minus the basic trapezoidal rule for $r{\geq}3$ by using zero mean-Gaussian.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.124-129
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• 2000

The flow of liquid and vapor is investigated in trapezoidal grooves. The effect of variable shear stress along the interface of the liquid and vapor is studied for both co-current and counter-current flows. Velocity contours and results fur the friction are obtained for both trapezoidal grooves. An approximate relation that was previously utilized for the friction for the liquid was modified to obtain accurate agreement with the results for trapezoidal grooves.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.245-257
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• 2007

We showed in [2] that if $r\leq2$, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to $h^{2r+3}$ using zero mean Gaussian distribution under the assumption that we have subintervals (for simplicity equal length) partitioning and that each subinterval has the length. In this paper, if $r\geq3$, we show that zero mean Gaussian distribution of average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by $Ch^8$.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.581-587
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• 2008

In this paper, to have a better a posteriori error bound of the average case error between the true value of I(f) and the Trapezoidal rule on subintervals using zero mean-Gaussian, we prove that a new average error between the difference of the true value of I(f) from the composite Trapezoidal rule and that of the composite Trapezoidal rule from the simple Trapezoidal rule is bounded by $c_rH^{2r+3}$ through direct computation of constants $c_r$ for r ${\leq}$ 2 under the assumption that we have subintervals (for simplicity equal length h) partitioning [0, 1].

• Steel and Composite Structures
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• v.3 no.3
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• pp.213-229
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• 2003

A high precision shear deformable triangular element has been proposed for free vibration analysis of composite trapezoidal plates. The element has twelve nodes at the three sides and four nodes inside the element. Initially the element has fifty-five degrees of freedom, which has been reduced to forty-eight by eliminating the degrees of freedom of the internal nodes through static condensation. Plates having different side ratios (b/a), boundary conditions, thickness ratios (h/a=0.01, 0.1 and 0.2), number of layers and fibre angle orientations have been analyzed by the proposed shear locking free element. Trapezoidal laminate with concentrated mass at the centre has also been analyzed. An efficient mass lumping scheme has been recommended, where the effect of rotary inertia has been included. For validation of the present element and formulation few results of isotropic trapezoidal plate and square composite laminate have been compared with those obtained from open literatures. The numerical results for composite trapezoidal laminate have been given as new results.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.754-756
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• 1987

In this paper, a new Harmonic Torque Factor(HTF) that represents torque ripple of induction motor is proposed. Trapezoidal PWM is analyzed to torque ripple by HTF and than we obtain optimum triangular factor at some carrier ratio. Six-step, sinusoidal PWM and Trapezoidal PWM are compared and evaluated for choosing a good control strategy of PWM inverter. It turns out that six-step inverter is better than sinusoidal PWM and Trapezoidal PWM when their carrier ratio is 9, and Trapezoidal PWM is superior to sinusoidal PWM. At induction motor is driven by PWM inverter, torque ripples are investigated by computer simulation using d-q two axis model. It is proved that a new Harmonic Torque Factor ix valid.

• Coupled systems mechanics
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• v.11 no.3
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• pp.233-257
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• 2022

This work presents a comparative study between two different models: trapezoidal and T-shaped combined footings. The comparative study between trapezoidal and T-shaped combined footings presented in this paper generatesresultsthat have an unparalleled accuracy for all foundation engineering problems. The main part of this research is to obtain the optimal area, reinforcing steel, and thickness of the trapezoidal and T-shaped combined footings using the new models. The comparison is made for two trapezoidal combined footings and two T-shaped combined footings ofreinforced concrete subjected to the same load.Themain findings are: themodelfortrapezoidal combined footings can be used for rectangular and triangular, and the T-shaped combined footings can be used for rectangular. The structure of the paper is asfollowsfirst a very complete state of the art with extensive referencesthat describesthe methodology used for the different models clearly, presents different numerical examples, results and at the end conclusions.