A General Formulation of the Optimal Frame Problem

1970 ◽  
Vol 37 (2) ◽  
pp. 356-360 ◽  
Author(s):  
D. E. Grierson ◽  
M. Z. Cohn
Keyword(s):  
Reinforced Concrete ◽  
Optimal Design ◽  
Elastic Limit ◽  
Limit Equilibrium ◽  
Steel Structures ◽  
Optimal Designs ◽  
Frame Problem ◽  
Material Consumption ◽  
Limit Stage ◽  
Simplifying Assumptions

Optimal design techniques have been extensively applied to steel structures and, to a lesser degree, to reinforced concrete structures. In the latter case, for given geometry and preassigned stiffnesses, optimal designs have been found which simultaneously satisfy (a) limit equilibrium (plastic limit stage), (b) serviceability (elastic limit stage), and (c) optimality (minimum material consumption). The limitations to these designs are: 1. A subsequent check of plastic compatibility may invalidate the design. 2. The resulting member stiffnesses may differ appreciably from the preassigned values. 3. A different geometry may result in a better solution while still satisfying all design criteria. The present paper attempts to eliminate these limitations through a more general formulation of the optimal frame problem wherein design plastic moments, member stiffnesses, and frame geometry are all treated as variables and are found for simultaneous satisfaction of (a) optimality, (b) limit equilibrium, (c) serviceability, (d) plastic compatibility, and (e) elastic compatibility. With some simplifying assumptions to linearize the problem, the general formulation is illustrated for a reinforced concrete continuous beam example. The resulting optimal design is compared with conventional elastic and plastic designs with respect to safety, serviceability, compatibility, and efficiency.

scholarly journals Multiobjective optimal design of reinforced concrete frames using two metaheuristic algorithms

2021 ◽  
Vol 9 (4B) ◽  
Author(s):  
Mehdi Babaei ◽  
◽  
Masoud Mollayi ◽  
Keyword(s):  
Reinforced Concrete ◽  
Optimal Design ◽  
Optimization Problem ◽  
Numerical Models ◽  
Steel Structures ◽  
Metaheuristic Algorithms ◽  
Rc Structures ◽  
Weighted Sum Method ◽  
Rc Frames ◽  
Single Objective

Genetic algorithm (GA) and differential evolution (DE) are metaheuristic algorithms that have shown a favorable performance in the optimization of complex problems. In recent years, only GA has been widely used for single-objective optimal design of reinforced concrete (RC) structures; however, it has been applied for multiobjective optimization of steel structures. In this article, the total structural cost and the roof displacement are considered as objective functions for the optimal design of the RC frames. Using the weighted sum method (WSM) approach, the two-objective optimization problem is converted to a single-objective optimization problem. The size of the beams and columns are considered as design variables, and the design requirements of the ACI-318 are employed as constraints. Five numerical models are studied to test the efficiency of the GA and DE algorithms. Pareto front curves are obtained for the building models using both algorithms. The detailed results show the accuracy and convergence speed of the algorithms.

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

scholarly journals Ultimate Compressive Strains and Reserves of Bearing Capacity of Short RC Columns with Basalt Fiber

2021 ◽  
Vol 11 (16) ◽  
pp. 7634
Author(s):  
Aleksandr V. Shilov ◽  
Alexey N. Beskopylny ◽  
Besarion Meskhi ◽  
Dmitry Mailyan ◽  
Dmitry Shilov ◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Bearing Capacity ◽  
Basalt Fiber ◽  
Lightweight Aggregate ◽  
Short Fiber ◽  
Hydraulic Press ◽  
Steel Reinforcement ◽  
Fiber Reinforced Concrete ◽  
Material Consumption ◽  
Short Columns

Increasing the bearing capacity of reinforced concrete structures, reducing material consumption, and ensuring quality are critical in modern construction. The article presents an experimental study of the ultimate compressive strains of short fiber basalt reinforced concrete columns and provides recommendations for increasing the bearing capacity using steel reinforcement bars with greater strength. The columns were tested in an upright position using a hydraulic press. Strains were measured with dial indicators and a strain gauge station. It was shown that the addition of 10% coarse basalt fiber increased the ultimate compressibility of concrete on ordinary crushed stone by 19.8%, and expanded clay concrete by 26.1%, which led to the strain hardening of concrete under compression by 9.0% and 12%, respectively. Ultimate compressive strains in fiber-reinforced concrete short columns with combined reinforcement increased 1.42 times in columns on a lightweight aggregate and 1.19 times on heavy aggregate. An increase in the ultimate compressibility of concrete makes it possible to use steel reinforcement with greater strength in compressed elements as the concrete crushing during compression occurs primarily due to the reaching of critical values by tensile stresses in the transverse direction. This makes it possible to manufacture structures with a higher load-bearing capacity and less material consumption. A practical example of the application of the proposed approach is given.

scholarly journals A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects

2019 ◽  
Vol 5 (344) ◽  
pp. 17-27
Author(s):  
Małgorzata Graczyk ◽  
Bronisław Ceranka
Keyword(s):  
Optimal Design ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Optimal Designs ◽  
Efficient Design ◽  
Spring Balance ◽  
Experimental Errors ◽  
Necessary And Sufficient

The problem of determining unknown measurements of objects in the model of spring balance weighing designs is presented. These designs are considered under the assumption that experimental errors are uncorrelated and that they have the same variances. The relations between the parameters of weighing designs are deliberated from the point of view of optimality criteria. In the paper, designs in which the product of the variances of estimators is possibly the smallest one, i.e. D‑optimal designs, are studied. A highly D‑efficient design in classes in which a D‑optimal design does not exist are determined. The necessary and sufficient conditions under which a highly efficient design exists and methods of its construction, along with relevant examples, are introduced.

Optimal Design of Plastic Structures for Fixed and Shakedown Loadings

1973 ◽  
Vol 40 (2) ◽  
pp. 595-599 ◽  
Author(s):  
M. Z. Cohn ◽  
S. R. Parimi
Keyword(s):  
Optimal Design ◽  
Loading Condition ◽  
Minimum Weight ◽  
Optimal Solution ◽  
Failure Criteria ◽  
Optimal Designs ◽  
Design Solution ◽  
Variable Loading ◽  
Framed Structures ◽  
A Value

Optimal (minimum weight) solutions for plastic framed structures under shakedown conditions are found by linear programming. Designs that are optimal for two failure criteria (collapse under fixed loads and collapse under variable repeated loads) are then investigated. It is found that these designs are governed by the ratio of the specified factors defining the two failure criteria, i.e., for shakedown, λs and for collapse under fixed loading, λ. Below a certain value (λs/λ)min the optimal solution under fixed loading is also optimal for fixed and shakedown loading. Above a value (λs/λ)max the optimal design for variable loading is also optimal under the two loading conditions. For intermediate values of λs/λ the optimal design that simultaneously satisfies the two criteria is different from the optimal designs for each independent loading condition. An example illustrates the effect of λs/λ on the nature of the design solution.

scholarly journals Testing parallelism for the four-parameter logistic model with D-optimal design

2020 ◽  
Vol 15 (3) ◽  
pp. 273-284
Author(s):  
Lin Ying ◽  
Hyun Seung Won
Keyword(s):  
Optimal Design ◽  
Logistic Model ◽  
Test Preparation ◽  
Test Sample ◽  
Optimal Designs ◽  
Model Parameters ◽  
Reference Standard ◽  
Response Curves ◽  
Classical Design ◽  
Intersection Union Test

In order to determine the potency of the test preparation relative to the standard preparation, it is often important to test parallelism between a pair of dose-response curves of reference standard and test sample. Optimal designs are known to be more powerful in testing parallelism as compared to classical designs. In this study, D-optimal design was implemented to study the parallelism and compare+ its performance with a classical design. We modified D-optimal design to test the parallelism in the four-parameter logistic (4PL) model using Intersection-Union Test (IUT). IUT method is appropriate when the null hypothesis is expressed as a union of sets, and by using this method complicated tests involving several parameters are easily constructed. Since D-optimal design minimizes the variances of model parameters, it can bring more power to the IUT test. A simulation study will be presented to compare the empirical properties of the two different designs.

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