Mathematical Relationship Research Articles

Compensation control strategy of hybrid driven three-dimensional elliptical vibration assisted cutting system based on piezoelectric hysteresis model

Three-dimensional elliptical vibration assisted cutting (3D-EVC) technology has been widely used in many high-precision technical fields due to its high-efficiency processing characteristics. However, the hysteresis and nonlinearity caused by the piezoelectric drive in the 3D-EVC system will impact the system control accuracy. This paper mainly studies the hysteresis and nonlinearity of the system, the feedforward-gray predicted fuzzy PID compound controller based on the generalized Bouc-Wen hysteresis nonlinear model and it is designed to realize the hysteresis compensation of the system. In this paper, input voltage and output displacement are represented by a mathematical relationship, and this relationship of the 3D-EVC system will be described by the generalized Bouc-Wen model. The improved flower pollination algorithm (IFPASO) is adopted in the identification process of parameters. A compound control strategy is formed based on traditional feed-forward control combined with fuzzy PID feedback control to compensate for hysteresis and nonlinearity, and an improved gray prediction model is introduced into the feedback loop. The 3D-EVC system tracking experiment verifies the effectiveness of the designed compound controller. Experiments have proved that the hysteresis component of the system is significantly reduced after the use of the compound controller for hysteresis compensation, and the system has a higher degree of stability.

Analysis of the application of BIM technology in the combination of interior design and smart home

Abstract This paper aims to explore the application in the combination of interior design and smart homes and constructs an intelligent algorithm of BIM+4D technology by analyzing BIM technology and its application in interior home design. The mathematical relationship of design duration is established on the basis of BIM+4D. Studied the system of BIM+ in interior home design and set up the standard and template of the interior home. The BIM+4D technology intelligent algorithm is used to analyze the survey data and verify the feasibility and development of BIM technology in the combination of interior design and smart homes. The result data shows that the amount of investment in smart home functions is increasing year by year, among which the amount of investment in smart home appliances has been at the forefront. Among the smart home functions, smart home appliances account for the highest percentage, accounting for 80; smart temperature control accounts for 50%, and smart audio accounts for 40%. Home Design VR and AR input amount growth rates of 10%, 20%, 40%, 50%, and 40%, respectively. The research in this paper is beneficial to promote better integration of interior design and smart homes.

Optimisation of rail profile and grinding pattern in the curve section of a subway

During routine rail maintenance, rail grinding of sharp curves is challenging. In particular, setting up the grinding pattern is essential. A rail-grinding pattern optimisation method is proposed based on the mathematical relationship between the grinding pattern parameters and geometric parameters of the rail grinding profile. In this method, the design variables and constraints are reasonably selected, and a multi-objective optimisation function considering the wheel-rail contact stress, wheel-rail lateral force, and rail grinding amount is established. The optimisation model is solved using a chaotic microvariation adaptive genetic algorithm. The optimisation method is applied to the repairable grinding of a worn rail in a metro curve section. The results demonstrate that using this method can realise an ideal grinding pattern with the expected grinding effect in addition to high accuracy and high optimisation speed. The wheel-rail contact characteristics, wear characteristics, and train dynamic performance are significantly improved after rail grinding; this is significant for conducting grinding operations and improving the train’s curve-passing ability. Therefore, this study provides theoretical guidance for formulating rail-grinding patterns.

Bypass Configurations of Membrane Humidifiers for Water Management in PEM Fuel Cells

Water management is an important criterion in the operation of proton-exchange membrane fuel cells to maintain the high performance and reliability of the system. The water content in the cathode air that is supplied to the cathode channel contributes to the membrane humidification and the transport of protons inside the membrane structure. In automotive applications, the supply air is typically driven through an external membrane humidifier to absorb more moisture from the recirculated cathode exhaust. In the literature, humidifiers and fuel cell stacks have been separately investigated without considering whole-system configurations for water management. This study investigates changes in the cathode air characteristics through a membrane humidifier and compares two configurations using a humidifier bypass of the supply flow and exhaust flow to adjust the cathode inlet air relative humidity. Each component in the system was modeled using mathematical relations and converted into blocks of inputs and outputs in MATLAB/Simulink for simulation. The bypass valve was demonstrated to effectively reduce the relative humidity of the supply air from the saturation rate to above 60%, with a bypass fraction of up to 0.6 in both configurations. These adjustments provide system flexibility to accommodate load changes and prevent flooding in the stack channels. Bypassing the supply air through the humidifier effectively maintained consistent cathode inlet humidity across a wide operational range. A 0.4 bypass fraction on the supply side sustained a relative humidity of around 80% for the whole range of operating flow rates. In contrast, the exhaust-side bypass had a smaller impact, and the relative humidity of the cathode air was reduced when the flow rate and bypass fraction increased. This study further supports the control system design to regulate the bypass fraction according to load transients.

How is the Mathematical Connection Ability of Post-Pandemic Class IV Elementary School Students in whole Numbers Material?

This study aims to analyze the mathematical connection ability of elementary school students in the material as whole counting numbers, and categories and based on indicators of mathematical connection ability. The subjects were students from Class IV as many as 114 elementary school students. This research is qualitative descriptive research using a purposive sampling technique. The research instruments used were a mathematical connection ability test and an interview. The indicators of the ability of mathematical connections measured include the relationship of mathematics with mathematics, the relationship of mathematics with other sciences, and the relationship of mathematics with everyday life. The results showed: (1) an overall mathematical connection ability of 24% including the category of less; (2) based on the category of mathematical connection ability showed that 49% of students are very less, 37% less Category, 7% Category enough, 7% Good category and 0% very good category; (3) the ability of mathematical connections based on indicators a) the relationship of mathematics with mathematics by 18% (very less Category), b) the relationship of mathematics with other sciences by 35% (less category), and c) the relationship of mathematics with everyday life by 17% (very less category). This shows that the ability of mathematical connections is still not owned by the fourth-grade students of elementary school and requires attention and further development by teachers and the school. Penelitian ini bertujuan unruk menganalisis kemampuan koneksi matematis siswa sekolah dasar pada materi bilangan cacah secara keseluruhan, kategori dan berdasarkan indikator kemampuan koneksi matematis. Subjek penelitian adalah siswa dari kelas IV sebanyak 114 siswa sekolah dasar. Penelitian ini merupakan jenis penelitian deskriptif kualitatif dengan menggunakan teknik purposive sampling. Instrumen penelitian yang digunakan adalah tes kemampuan koneksi matematis dan wawancara. Indikator kemampuan koneksi matematis yang diukur meliputi: hubungan matematika dengan matematika, hubungan matematika dengan ilmu lain dan hubungan matematika dengan kehidupan sehari-hari. Hasil penelitian menunjukan: (1) secara keseluruhan kemampuan koneksi matematis sebesar 24% termasuk kategori kurang; (2) berdasararkan kategori kemampuan koneksi matematis menunjukan bahwa 49% siswa berkemampuan sangat kurang, 37% kategori kurang, 7% kategori cukup, 7% kategori baik dan 0% kategori sangat baik; (3) Kemampuan koneksi matematis berdasarkan indikator a) hubungan matematika dengan matematika sebesar 18% (kategori sangat kurang), b) hubungan matematika dengan ilmu lain sebesar 35% (kategori kurang), dan c) hubungan matematika dengan kehidupan sehari-hari sebesar 17% (kategori sangat kurang). Hal ini menunjukan bahwa kemampuan koneksi matematis masih belum dimiliki oleh siswa kelas IV sekolah dasar dan memerlukan perhatian serta pengembangan lebih lanjut oleh guru maupun pemangku kebijakan lainnya.

Pressure control for pneumatic pressing roller in automated fiber placement

In automated fiber placement (AFP), the contact pressure between the roller and the mold is an important process parameter. Too small or too large contact pressure will result in unacceptable laying defects. This paper focuses on the control method of contact pressure in AFP. Firstly, the dynamic model of the pressing foot mechanism is established, and a mathematical relationship of input air pressure and output force is developed. Then, a self-tuning PI control algorithm is used to implement servo control of the roller output force based on the Slowly Time-Varying Recursive Identification Algorithm. Also, using Abaqus/CAE, the mapping relationship between the contact area and measurements from displacement sensors is established to predict the contact area in real time. Finally, the contact pressure control method is established by combining the servo control method of contact force and the prediction method of contact area. Experimental results show that the constant pressure control method can effectively stabilize the contact pressure, with a pressure fluctuation of less than 4% under the experimental conditions set in this paper.

Prediction of tribology in (Mg2Si+TiB2)/A356 composites based on RSM method and correlative with topographical characteristics

This work deals with the prediction of tribological performance in (Mg2Si+TiB2)/A356 composites. In this work, tribological properties are also correlated with topographical characteristics. The effect of several input factors such as load, sliding distance and TiB2 wt% on tribological characteristics of (Mg2Si+TiB2)/A356 composites was explored by Response Surface Methodology (RSM). Central composite design (CCD) with three input factors and three levels of variables in RSM was used to develop a statistical model. RSM suggests a quadratic model to express a mathematical relationship between input factors to assess wear rate and coefficient of friction (COF). Analysis of variance (ANOVA) was applied to investigate the influence of input factors on wear rate and COF and found that most significant variable that influences wear rate and COF is applied load followed by TiB2 wt% and sliding distance. The desirability function approach is applied to optimized input variables to minimize wear rate and COF. Optimum wear rate is noticed at input variables of 26 N load, 2766 m sliding distance and 3.36 wt% of TiB2 and optimum COF was observed at 29 N of load, 2233 m sliding distance and 1 wt% of TiB2. A confirmatory test was conducted to validate the developed model and observed that experimental results matched the predicted value with an error of less than 5%. SEM and AFM examined surface topography of wear surfaces to understand the wear mechanism and surface features at various input factors. Microstructural features were also examined under optical microscope and SEM, revealing that increased TiB2 content in hybrid composite refined primary Mg2Si and eutectic Mg2Si phase and resulted in increased hardness and improved tribological behaviour of hybrid composite.

Mathematical Model for Growth and Rifampicin-Dependent Killing Kinetics of Escherichia coli Cells.

Antibiotic resistance is a global health threat. We urgently need better strategies to improve antibiotic use to combat antibiotic resistance. Currently, there are a limited number of antibiotics in the treatment repertoire of existing bacterial infections. Among them, rifampicin is a broad-spectrum antibiotic against various bacterial pathogens. However, during rifampicin exposure, the appearance of persisters or resisters decreases its efficacy. Hence, to benefit more from rifampicin, its current standard dosage might be reconsidered and explored using both computational tools and experimental or clinical studies. In this study, we present the mathematical relationship between the concentration of rifampicin and the growth and killing kinetics of Escherichia coli cells. We generated time-killing curves of E. coli cells in the presence of 4, 16, and 32 μg/mL rifampicin exposures. We specifically focused on the oscillations with decreasing amplitude over time in the growth and killing kinetics of rifampicin-exposed E. coli cells. We propose the solution form of a second-order linear differential equation for a damped oscillator to represent the mathematical relationship. We applied a nonlinear curve fitting solver to time-killing curve data to obtain the model parameters. The results show a high fitting accuracy.

Performance research and optimization of marine dual-fuel engine based on RSM and NSGA-II

ABSTRACT In order to improve the economic efficiency of the ship when sailing and reduce the engine optimization cost. We propose the Response Surface Methodology (RSM) combined with NSGA-II to optimize the engine parameters. First, a simulation model of a marine four-stroke dual-fuel engine is established in AVL-BOOST software. Then, control parameters such as engine speed, exhaust valve opening (EVO) and compression ratio (CR) are planned by design of experiments. The response surface model was established in Design-Expert software. The significant influence of control parameters on performance parameters was studied by analysis of variance (ANOVA). Finally, with the output power, indicated fuel consumption rate and nitrogen oxide emissions as the optimization objectives. Non-dominated Sequential Genetic Algorithm (NSGA-II) is used to optimize the parameters to improve engine performance and reduce emissions. The results show that the established response surface model has good prediction accuracy. The response surface model visualizes the mathematical relationship between the control parameters and the optimization targets. The ANOVA results show that engine speed, EVO and CR have significant effects on engine performance and emissions. The optimization results show that the engine speed is 793 rpm, the EVO is 145°CA, and the CR is 12.3. Compared to standard settings, the optimized data shows a 3.4% increase in power, a 0.3% reduction in ISFC, and a 6.2% reduction in nitrogen oxide (NOx) emissions. The combination of response surface analysis and NSGA-II algorithm to optimize engine performance and emissions is thereby a feasible method.

A Robust Adaptive Control Strategy for Electro-hydraulic Servo Based on Friction Compensation

Background: The electro-hydraulic servo system has the advantages of high stiffness, fast response speed, high precision and power-to-weight ratio. Objective: In this patent, an adaptive robust control strategy based on friction compensation is proposed for insufficient control accuracy due to a large number of nonlinearities and uncertainties in the system. Methods: In this patent, the mathematical relationship between the physical quantities of the valve-controlled cylinder is analyzed. Then the mathematical model of valve controlled cylinder considering the main nonlinearity and uncertainty of the system is established. The fuzzy proportion-integral-derivative, deterministic robust, and adaptive robust single-cylinder trajectory tracking controllers are designed and the tracking performance of different reference trajectories is analyzed by MATLAB/Simulink software. Results: In this patent, all the three controllers can track the reference trajectories smoothly. Adaptive robust control strategy can make the uncertain parameters of system converge and approach truth value. Conclusion: In this patent, the adaptive robust control strategy has the function of online parameter adjustment. When tracking accuracy is taken as the index, its tracking effect is better than fuzzy proportion-integral-derivative and deterministic robust.

Effects of taper ratio on the aerodynamic forces and flow field of two tandem square cylinders

To explore the influence of taper ratio on aerodynamic characteristics of tandem square cylinders, three-dimensional (3D) large eddy simulations of flow around two tandem square cylinders at the Reynolds number (Re) = 2 × 103 are carried out with a spacing ratio G/D = 4, where G is the cylinder center-to-center distance and D is the cylinder width. Different taper ratios of ξ = 0%, 5%, 10%, and 15% are considered. The influence of taper ratio on aerodynamic coefficient, wind pressure coefficient, mean, and instantaneous flow fields are comprehensively studied. The mechanism of variation in flow fields is revealed, and the mathematical relationship between the taper ratio and aerodynamic characteristics is established, which can provide theoretical reference for design and construction of tandem structures. The results indicate that the taper ratio has significant influence on the mean force coefficient, fluctuating force coefficient, surface mean and fluctuating pressure coefficients, and vortex shedding frequency (fvs). As increase in the taper ratio, the mean force in the along-wind direction, fluctuating force in the across-wind direction, and surface pressure of the two cylinders will be decreased, but the vortex shedding frequency will be increased. The taper ratio has negligible influence on the flow separation location of the upstream cylinder. However, reattachment location of the shear layer moves backward along the leeward surface of the downstream cylinder, and width of the shear layer gradually becomes narrower and closer to surface of the two cylinders. The vortex shedding strength and vortex energy distribution of the two cylinders will be reduced as a result of the narrower shear layer. Meanwhile, coherence and periodicity of the vortex shedding will also be weakened, which results in reduction in the aerodynamic forces and increase in the vortex shedding frequency.

Research on the Co-simulation System of Subway Control Circuits

In order to solve the problems of complex control logic and the difficulty of simulating function modules due to the high coupling degree of subway control circuits, a subway control circuit co-simulation system is designed in this paper. By analysing the components data and connection relationship in the subway control circuit schematic diagrams, the network topologies are automatically generated, and the mathematical relationships between nodes, branches and components states are established, so as to build a complete logical control model. The depth-first search (DFS) algorithm is adopted to search the effective path across the topology, the event management unit is added to solve the linkage control of the relay, and the logic function simulation of the function module is realized by embedded script. Finally, the feasibility of the simulation system is verified through the simulation test of the subway door control circuits and the analysis of the simulation results. The system is conducive to the functional test and algorithm verification at the subway design stage, and has a good application prospect in the field of subway driver training.

Plant-Independent Current Sensor Gain Error Compensation for Highly Dynamic Drives

In this article, gain errors in current sensing for highly dynamic three-phase drives with three current sensor measurements are compensated without the aid of the machine plant model. As three current sensors are used, redundant information from the neutral current measurement is extracted by constructing its mathematical relation with the measured time-varying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> current. The proposed method compensates for non-symmetrical current sensor gain errors even in the presence of offset errors. A Recursive Sliding Window Least Square method is proposed to minimize the computation effort such that the method is suitable to be applied online. It does not incorporate a low-pass filter or averaging method based on electrical speed, making it suitable for highly dynamic applications. It is able to be applied in any three-phase AC machine, as the machine plant is not considered. Analysis, simulation and experimental results obtained from the hardware prototype by mimicking the actual application of high-precision mechatronics demonstrate the validity of the proposed method.

A Reduced-Order Decoupling Method Applied to Efficient Junction Temperature Simulation Model in Multichip Devices

As the power density of power modules increases, the cross-heating effects in multichip modules become severe, which intensifies the local overheating stress. To accurately predict the dynamic thermal characteristics of the multichip modules, this paper establishes the mathematical relationship between the resistance-capacitance (RC) parameters and the thermal diffusion angle to obtain accurate RC parameters. The decoupling of the self-heating and cross-heating effects is realized according to the dynamic power flow in the RC thermal network, reducing the transient thermal impedance matrix to the steady-state thermal resistance matrix. In this way, the 3-D cross-heating effect on the junction temperature is characterized by the 1-D RC thermal network. Then, an efficient junction temperature simulation model based on the reduced-order decoupling method is proposed. This article also identifies the variation law of RC parameters with boundary conditions. Compared with existing models that need transient information, the model parameter extraction process requires only the steady-state information of the finite element method (FEM) and fewer RC parameters, which improves the parameter extraction efficiency by more than 87 times. In addition, compared with the FEM model, the transient junction temperature prediction efficiency is improved by more than 994 times. Finally, based on a 1200V/50A half-bridge module, an electrothermal coupling model is constructed and applied to a three-phase two-stage inverter circuit. The results verify the accuracy and effectiveness of the proposed model, demonstrating that the junction temperature error between the proposed model and the experimental result is less than 5%.

Relationship between Infection Caused by the Apicomplex Protozoan Nematopsis sp and the Weight of White Shrimp Litopenaeus vannamei in a Cultivation System

There are many types of diseases and etiological agents that affect the health of the cultivated white shrimp Litopenaeus vannamei (viruses, bacteria, fungi, and parasites), with parasitic diseases being of great relevance. From this perspective, the main parasitic diseases in cultured shrimp are given by protozoa, mainly Apicomplexa (Gregarines) and Ciliophora (Epibionts or Ectoparasites). The objective of this research is to establish the mathematical relationship between the infection caused by the apicomplexan protozoan Nematopsis sp and the weight of the white shrimp Litopenaeus vannamei in a cultivation system. This work was carried out on the western coast of the state of Falcón (Venezuela), where several shrimp farms are located. The animals were randomly sampled in the ponds and immediately taken to the laboratory for analysis (presence of the parasite and weight). The results indicate that the physicochemical parameters of the water remained stable during the test. The prevalence of parasitosis was 25% in May/June, 28% in July, 27.64% in August, 35.5% in September and 32% in October. In addition, it was observed that the average weight of shrimp increased over time, being 0.313 in May/June, 3.2765 in July, 7.4831 in August, 11.3776 in September and 12.71 in October. The R value was 0.119 indicating little dependence on the variables, and an R2 of 0.0143 showing that parasitosis only had an effect on the weight of 1.43% of the infected animals.

Evaluation of Ensemble Snowfall Forecasts Using Operationally Used Snow-to-Liquid Ratios in Five Winter Storms

Abstract The prediction of snow accumulation remains a forecasting challenge. While the adoption of ensemble numerical weather prediction has enabled the development of probabilistic guidance, the challenges associated with snow accumulation, particularly snow-to-liquid ratio (SLR), still remain when building snow-accumulation tools. In operations, SLR is generally assumed to either fit a simple mathematical relationship or conform to a historic average. In this paper, the impacts of the choice of SLR on ensemble snow forecasts are tested. Ensemble forecasts from the nine-member High-Resolution Rapid Refresh Ensemble (HRRRE) were used to create 24-h snowfall forecasts for five snowfall events associated with winter cyclones. These snowfall forecasts were derived from model liquid precipitation forecasts using five SLR relationships. These forecasts were evaluated against daily new snowfall observations from the Community Collaborative Rain Hail and Snow network. The results of this analysis show that the forecast error associated with individual members is similar to the error associated with choice of SLR. The SLR with the lowest forecast error showed regional agreement across nearby observations. This suggests that, while there is no one SLR that works best everywhere, it may be possible to improve ensemble snow forecasts if regions where SLRs perform best can be determined ahead of time. The implications of these findings for future ensemble snowfall tools will be discussed. Significance Statement Snowfall prediction remains a challenge. Computer models are used to address the inherent uncertainty in forecasts. This uncertainty includes aspects like the location and rate of snowfall. Meteorologists run multiple similar computer models to understand the range of possible weather outcomes. One aspect of uncertainty is the snow-to-liquid ratio, or the ratio of snow depth to the amount of liquid water it melts into. This study tests how common predictions of snow-to-liquid ratio impact snowfall forecasts. The results show that snow-to-liquid ratio choices are as impactful as the models’ differing snow rate or snow location forecasts, and that no particular snow-to-liquid ratio is most accurate. These results underscore the importance of better snow-to-liquid ratio prediction to improve snowfall forecasts.

Teaching the connections between music and mathematics

Mathematics is often perceived by students as being difficult. However, when they see how math and music are intimately related, their attitude often changes. Some of the most fundamental aspects of music are described by math. For example, the Circle of Fifths closely reflects musical structure and is used to create scales and chord progressions. The Circle is structured around the mathematical relations of frequency ratios of the corresponding notes in a 12-tone scale. The reactions to music of consonance and dissonance are related to the relative ratios of the notes in a chord or note sequence in a piece. The connection between music and math forms the basis for creating instruments that play the music. I will suggest ways to present these concepts to students for their greater appreciation of music and math.

The Prophetic Speeches (Hadith) on Sciences and Scientists: Application of the "Text from Text and D+" Theory

This study aims to apply the theory of "Text from Text and the Plus Dimension" in the analysis of the Prophetic discourse found in the section on the virtues of knowledge and scholars from Imam Sahih al-Bukhari's book. This section covers several topics, including the virtue of gathering for the sake of learning, the superiority of a scholar over a worshipper, the excellence of jurisprudence in the religion of Allah, the acquisition of knowledge through the passing away of scholars, the merit of inviting people to Allah, the continuing benefit of beneficial knowledge after a scholar's demise, the warning against seeking knowledge for purposes other than Allah, and the Prophet seeking refuge from knowledge that brings no benefit. This is an applied analytical study that aims to elucidate the scientific miraculousness in the Prophetic hadiths and explain the meanings of the Prophetic sayings in harmony with scholars and the majority. It also seeks to derive moral lessons from the hadiths and reveal meanings that might be ambiguous or hidden using the "Text from Text and the Plus Dimension" theory in the analysis of the Prophetic discourse. The study arranges the sentences of the hadiths in the section on the virtues of knowledge and scholars from Sahih al-Bukhari's book and examines their meaning and rhetorical composition. It links them with mathematical geometric relationships such as rotation, expansion through magnification and contraction, withdrawal (beginning with the beginning), and reflection (beginning with the end). The study adopts an analytical and explanatory methodology to achieve its objectives, and the corpus of the study consists of Prophetic hadiths from the section on the virtues of knowledge and scholars from Sahih al-Bukhari's book, along with all its topics. This research builds upon two previous studies where the theory was applied to analyze the Prophetic discourse: "Inviting to Contemplate the Prophetic Discourse: Text from Text and the Extra Dimension in the Analysis of the Prophetic Discourse" (Al-Rawajfeh, 2020) and "The Theory of Text from Text and the Extra Dimension in the Analysis and Miraculousness of the Prophetic Discourse: An Application to the Book of Faith from Sahih al-Bukhari" (Al-Rawajfeh and Al-Jubbah, 2023)

Un caso de transversalidad con regresiones y ecuaciones en el crecimiento de una planta de maíz amarillo (Zea mays L.)

For educational purposes for student learning and the cross-sectional relationship of mathematics with corn production, this research is developed as a case study of the Centro Bachillerato Tecnológico Agropecuario 116 (CBTa 116) located in the municipality of Angostura, Sinaloa. Corn is a fundamental product of the primary sector of the municipality and the state, therefore, the case study is directly linked to the context, thus allowing, to acquire an integral learning of the growth process of a yellow corn plant (Zea mays) and considering transversality as a focal point of mathematics, through research and implementation in the sowing of said seed through a quasi-experimental design. The process to follow was sowing, germination and monitoring the growth of the plant, recording the data in a logbook for 18 days. Subsequently, a table and graphs with regression results were developed to obtain its equation and R2 (attachment to the data) using Excel software, thereby generating exponential, linear, logarithmic and potential equations. The results obtained showed that the linear equations were the ones that were most attached to the growth that the plants showed with the equation y= 1.9319x + 0.4582 and with an R2 of 0.9893.

Efficient buckling and post-buckling analysis of porous FG sandwich beams by new RPIM-HOCM mesh-free approach

The main purpose of this paper is to analyze buckling and post-buckling behavior of porous functionally graded (FG) beams and sandwich beams using a new efficient optimal mesh-free high order algorithm. The proposed solver combines mesh-free approach based on radial point interpolation method with high order continuation method (RPIM-HOCM). It is assumed that the FG beam and FG layers of sandwich beam are made from a mixture of ceramic and metal such that bottom surface of the plate is metal-rich, whereas top surface is ceramic-rich. So, constitutive equation as well as material properties are considered to change smoothly and gradually in the thickness direction via a mathematical relationship distribution. Non-linear strong form of the beam buckling problem which is based on the first-order shear deformation theory (FSDT) is derived using the virtual displacements theorem. The proposed coupling (RPIM-HOCM) is presented and validated firstly by comparing obtained numerical results with those computed using a reference algorithm. Then, RPIM-HOCM solver is used to investigate the effect of power-law index, porosity distribution, span-to-height ratio, boundary conditions and skin-core–skin thickness ratio on critical buckling load and post-buckling behavior.