Noninteger Derivative Order Analysis on Plane Wave Reflection from Electro-Magneto-Thermo-Microstretch Medium with a Gravity Field within the Three-Phase Lag Model

The present research paper illustrates how noninteger derivative order analysis affects the reflection of partial thermal expansion waves under the generalized theory of plane harmonic wave reflection from a semivacuum elastic solid material with both gravity and magnetic field in the three-phase lag model (3PHL). The main goal for this study is investigating the fractional order impact and the applications related to the orders, especially in biology, medicine, and bioinformatics, besides the integer order considering an external effect, such as electromagnetic, gravity, and phase lags in a microstretch medium. The problem fractional form was formulated, and the boundary conditions were applied. The results were displayed graphically, considering the 3PHL model with magnetic field, gravity, and relaxation time. These findings were an explicit comparison of the effect of the plane wave reflection amplitude with integer derivative order analysis and noninteger derivative order analysis. The fractional order was compared to the correspondence integer order that indicated to the difference between them and agreement with the applications in biology, medicine, and other related topics. This phenomenon has more applications in relation to the biology and biomathematics problems.

Comparative Analysis and Design of Bridge Pier for Various Geometries Along Height Comparing the Parameters Deflection and Bending Stresses

Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

Comparative Analysis and Design of Bridge Pier for various Geometries along height

Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

Estimates of Generalized Hessians for Optimal Value Functions in Mathematical Programming

We consider the optimal value function of a parametric optimization problem. A large number of publications have been dedicated to the study of continuity and differentiability properties of the function. However, the differentiability aspect of works in the current literature has mostly been limited to first order analysis, with focus on estimates of its directional derivatives and subdifferentials, given that the function is typically nonsmooth. With the progress made in the last two to three decades in major subfields of optimization such as robust, minmax, semi-infinite and bilevel optimization, and their connection to the optimal value function, there is a need for a second order analysis of the generalized differentiability properties of this function. This could enable the development of robust solution algorithms, such as the Newton method. The main goal of this paper is to provide estimates of the generalized Hessian for the optimal value function. Our results are based on two handy tools from parametric optimization, namely the optimal solution and Lagrange multiplier mappings, for which completely detailed estimates of their generalized derivatives are either well-known or can easily be obtained.

Construction of Uniaxial Interaction Diagram for Slender Reinforced Concrete Column Based on Nonlinear Finite Element Analysis

Slender reinforced concrete column may fail in material failure or instability failure. Instability failure is a common problem which cannot be analyzed with first-order analysis. So, second-order analysis is required to analyze instability failure of slender RC column. The main objective of this study was to construct uniaxial interaction diagram for slender reinforced concrete column based on nonlinear finite element analysis (FEA) software. The key parameters which were studied in this study were eccentricity, slenderness ratio, steel ratio, and shape of the column. Concrete damage plasticity (CDP) was utilized in modeling the concrete. Material nonlinearity, geometric nonlinearity, effect of cracking, and tension stiffening effect were included in the modeling. The results reveal that, as slenderness ratio increases, the balanced moment also increases, but the corresponding axial load was decreased. However, increasing the amount of steel reinforcement to the column increases the stability of the column and reduces the effect of slenderness ratio. Also, the capacity of square slender RC column is larger than rectangular slender RC column with equivalent cross section. However, the result is close to each other as slenderness ratio increased. Finally, validation was conducted by taking a benchmark experiment, and it shows that FEA result agrees with the experimental by 85.581%.