Optimum design of perforated symmetric laminates using evolutionary algorithm

To calculate the percentage depth dose of any irregular shape electron beam using modified lateral build-up-ratio method. Percentage depth dose (PDD) curves were measured using 6, 9, 12, and 15MeV electron beam energies for applicator cone sizes of 6×6, 10×10, 14×14, and 14×14cm2 . Circular cutouts for each cone were prepared from 2.0cm diameter to the maximum possible size for each cone. In addition, three irregular cutouts were prepared. The scanning was done using a water tank and two diodes - one for the signal and the other a stationary reference outside the tank. The water surface was determined by scanning the signal diode slowly from water to air and by noting the sharp change of the percentage depth dose curve at the water/air interface. The lateral build-up-ratio (LBR) for each circular cutout was calculated from the measured PDD curve using the open field of the 14×14 cm2 cone as the reference field. Using the LBR values and the radius of the circular cutouts, the corresponding lateral spread parameter (sigma) of the electron shower was calculated. Unlike the commonly accepted assumption that sigma is independent of cutout size, it is shown that the sigma value increases linearly with circular cutout size. Using this characteristic of sigma, the PDD curves of irregularly shaped cutouts were calculated. Finally, the calculated PDD curves were compared with measured PDD curves. In this research, it is shown that sigma increases with cutout size. For radius of circular cutout sizes up to the equilibrium range of the electron beam, the increase of sigma with the cutout size is linear. The percentage difference of the calculated PDD from the measured PDD for irregularly shaped cutouts was under 1.0%. Similar Result was obtained for four electron beam energies (6, 9, 12, and 15MeV).

In this research, natural frequency response of functionally-graded multilayer graphene-reinforced composite plate with circular cutout reinforced by orthogonal stiffeners is investigated for the first time. The structure is surrounded by Winkler-type elastic support. The plate is composed of polymethyl methacrylate (PMMA) as matrix material and reinforced by graphene platelets (GPLs). The material of the orthogonal stiffeners is the same as that for the matrix. Rule of mixtures and Halpin–Tsai approach are applied to estimate the effective material properties of the composite plate. Third-order shear deformation plate theory and finite element procedure is employed to obtain the element matrices of the structure. Natural frequencies and mode shapes of the stiffened plate are reported for different variables such as nanofillers dispersion patterns, width and height of the stiffeners, aspect ratio of plate, plate thickness ratio, weight fraction of nanofillers, number of stiffeners, boundary conditions, elastic foundation stiffness parameter and size of circular cutout. The obtained results denote that with the addition of a set of stiffeners, fundamental frequency enhanced up to 32.3% with just about 10% increase of mass.

This paper is concerned with the failure characteristics and the failure loads of laser welds in a SPRC340 1.2t steel sheet under combined normal and shear loading conditions. The quasi-static and dynamic failure tests were carried out under nine different combined normal and shear loads including a pure-normal load and a pure-shear load. Especially for the pure-shear condition, a testing fixture was newly designed in order to evaluate the strength of a laser-welded region fabricated by the same welding condition as a two-layered lap joint. The failure load and the failure behavior of laser welds were investigated in each loading condition. Dynamic effects on the failure load of laser welds, which are critical for structural crashworthiness, were also examined based on the experimental data. In order to evaluate the effect of the strain rate on the failure contour of laser welds under the combined normal and shear loads, the failure loads measured from the experiment were decomposed into two components along the normal and shear directions.

Failure loads of spot welds under combined opening and shear static loading conditions

Local FEM Analysis of Composite Beams and Plates: Free-Edge effect and Incompatible Kinematics Coupling

Fatigue data obtained under biaxial loading conditions for adhesively bonded joints are used to plot S-N type diagrams to assess the effects of biaxiality in loading. Independently Loaded Mixed-Mode Specimens (ILMMS) are used for data collection purposes. These specimens are basically two (steel) beams bonded together to be fatigue loaded under cantilever (opening) mode while a simultaneous but physically separate inplane (static) shear load is also induced with the aid of a small hydraulic piston embedded in the specimen. Application of such static shear loads on the bonded joint results in S-N behavior different than that obtained with opening load only. The model adhesives used are Metlbond 1113-2 and Metlbond 1113 solid film thermoset adhesives similar to those commonly used in aircraft and aerospace industries. The former is an elastomer-modified epoxy adhesive and the latter is identical except that it contains a synthetic carrier cloth. Thus, the effect of carrier cloth in adhesive's S-N behavior is also assessed. Analytically, the classical linear log-log representation of the adhesive S-N data in log PImax versus log Nc or log PII versus log Nc formats is explored. The modifications necessary to reflect the effects of biaxiality in loading and also the presence of a carrier cloth are assessed. The fatigue failure results are also compared with the results obtained under monotonic biaxial loading conditions.

Damage assessment studies in CFRP composite laminate with cut-out subjected to in-plane shear loading

The elastic stress field around a circular elastic inclusion in an infinite functionally graded material (FGM) panel that is subjected to a uniform static anti-plane shear loading at infinity is considered. Assuming the rigidity modulus of the FGM panel to be exponential, the analytical solutions of stress and strain distribution around the circular elastic inclusion are obtained by using the variable separation method. Due the generality of the elastic inclusion, other geometrical discontinuities, such as hole and rigid inclusion, can be seen as special cases of circular elastic inclusion when the inclusion rigidity modulus takes a suitable value. Therefore, the present solutions ana- lytically reduce to some classical solution in some special cases. The present analytical solutions are compared with the existing exact solutions to verify them. Finally, the effects of the relative inclusion rigidity modulus ratio and the inhomogeneous rigidity modulus ratio on the stress distribution and the concentration factor are systematically investigated.

Use of composites for a range of structural application in aircrafts, space-crafts, automobiles, etc., has widely spread in the last few years. Other than weight reduction, cut-outs provide pathways to link different aircraft parts. In this paper, an experimental investigation was conducted to study the effect of a cut-out on the tensile strength of the fiber glass/ epoxy composite plate. Geometry of the cut-out is one of the important factors which can critically alter the mechanical properties. So, cut-outs with various geometrical shapes such as square and circle were introduced in the fiber glass/ epoxy composite plate and tensile tests were performed under ambient conditions. It was determined from the tests that specimens with circular cut-out have higher tensile strength as compared to specimens with square cut-out.

A B S T R A C T Stress concentration is the localization of stresses due to discontinuation or abruption in the geometry. To find the localized stresses, Stress Concentration Factor (SCF) is used. SCF depends on the material and geometry of the specimen. In the present paper an orthotropic plate with a central circular cutout subjected to normal pressure is studied. Based on material properties variation of the non-dimensional parameters E2/E1, G12/E1 and µ12 have been considered within their feasible range. The effect of these nondimensional parameters at different values of polar angle on SCF is studied here. Formulation of mathematical equation for SCF has been done in MATLAB and subsequently results are presented here. The work successfully highlights that for orthotropic material (unlike isotropic materials) SCF depends on material properties. It increases with increase in E2/E1 ratio and decreases with increase in µ12 and G12/E1 ratio.

Purpose This paper aims to construct a quantitative model using response surface methodology and optimize the structural parameters of Chip Scale Package (CSP) solder joints through genetic algorithms. This approach enhances the reliability of CSP solder joints under coupled tensile and shear loading, thereby improving the overall reliability of electronic products. Design/methodology/approach A finite element model for CSP solder joints was established using ANSYS software. Stress−strain finite element analysis was performed under coupled tensile and shear loading conditions. The resulting stress and strain distribution within the solder joints under this coupled loading was obtained. An experimental platform was constructed, and stress measurement experiments on CSP solder joints under coupled tensile and shear loading were conducted, thereby validating the accuracy of the simulation results. Taking solder joint diameter, solder joint height, pad diameter and pad thickness as design parameters, and the coupled tensile-shear stress value in the CSP solder joint as the objective, 27 sets of parameter level combinations were designed using the Response Surface Methodology. Corresponding finite element models for these 27 sets were established and subjected to simulation analysis under coupled tensile and shear loading. The relationship between the 27 sets of coupled stress values and the CSP solder joint morphological parameters was fitted using the response surface method, establishing a quantitative relationship equation. This equation was then subjected to optimization analysis using a genetic algorithm. Findings The results indicate that the location of maximum stress and strain is at the interface between the solder joint and the lower pad, which is identified as a potential failure site. The theoretically optimal combination of morphological parameters for the CSP solder joint, obtained via the genetic algorithm, is as follows: solder joint diameter of 0.3180 mm, solder joint height of 0.2302 mm, pad diameter of 0.2286 mm and pad thickness of 0.0168 mm. Simulation verification of this optimal parameter set demonstrated that the coupled tensile and shear stress value under the optimal combination is superior to those obtained from the 27 simulation experiments. This successfully achieves the morphological parameter optimization of CSP solder joints under coupled tensile and shear loading. Originality/value The relationship between the 27 sets of coupled stress values and the CSP solder joint morphological parameters was fitted using the response surface method, establishing a quantitative relationship equation. This equation was then subjected to optimization analysis using a genetic algorithm.

A theoretical investigation was made into the effect of a rivet-attached stringer on the stress concentrations in a thin elastic sheet with a circular cutout. The sheet and stringer are loaded (at infinity) by a uniform tensile stress parallel to the stringer. The results are expressed in terms of a “correction factor.”

Purpose: To compare electron cutout factor (COF) measured with various dosimeters for different cone sizes. Method and Materials: The COFs for various electron fields were measured on a Varian‐2300EX linear accelerator at 6, 9, 12, 16 and 20 MeV. A thimble ion chamber, plane parallel chamber, thermoluminescent dosimeters (TLDs), EDR film, X Omat‐V (XV) film, GafChromic film and Thomson‐Nielsen mosfets were used to measure COFs. Each detector was placed along the beam's central axis at 100 cm from the source. Measurements were made in solid water at dmax for 6×6, 10×10 and 20×∼20 cone sizes with circular cutouts. The thimble chamber was used as the standard to compare COF measurements. The raw measurements made with the two chambers and the diodes were used to determine the COFs. Films were analyzed with RIT software and TLDs were read the next day to determine COFs. Results: Measurements for the 10×10 and 20×20 cone sizes agreed within 3.5% between all the dosimeters and the thimble chamber. Measurements made for the 6×6 cone and cutout were more than 3.5% from those made with the thimble chamber. There was better agreement for COF measurements between the mosfets, TLDs, EDR film and XV film. Conclusion: This study takes a look at the various dosimeters available at the clinic that can be used for determining electron cutout factors. For most cutout sizes, ionization chambers, mosfets, TLDs, EDR, XV and GafChromic film can be used to measure the COFs for all electron energies. For small field sizes, the use of TLDs, mosfets, and film can give more accurate COFs.

This research undertakes a comprehensive parametric study of the ASTM D 6641 Combined Loading Compression (CLC) test fixture from Wyoming Test Fixtures (WTF) using numerical analysis to evaluate various test parameters associated with compression testing of unidirectional test specimens. A two-dimensional finite element analysis of the D 6641 CLC fixture was used to identify loading conditions and tabbing configurations that minimized the peak axial, shear, and through-thickness stress concentrations in the test specimen. Combined shear and end loading appears to offer a good compromise between reducing the tab tip stress concentrations inherent in shear loading, and avoiding premature failure by end brooming associated with end loading. Thin, tapered tabs made of compliant materials were found to have the smallest stress concentrations at the tab tip. Specimens with these tab configurations should yield higher measured compressive strengths since premature failure at the tab tip is less likely to occur. Partial debonding of the tab tip was found to increase the stress concentration compared to the fully-bonded case, but to move its location away from the gage section of the specimen. Tab tip debonding should be avoided for compressive strength testing.

This research investigates the mechanical behavior and damage evolution in cross-ply basalt fiber composites subjected to different loading modes. A modified Arcan rig for simultaneous acoustic emission (AE) monitoring was designed and manufactured to apply quasi-isotropic shear, combined tensile and shear loading, and pure tensile loading on specimens with a central notch. Digital image correlation (DIC) was applied for high-resolution strain measurements. The measured failure strengths of the bio-composite specimens under different loading angles are presented. The different competing failure mechanisms that contribute to the local reduction in stress concentration are described. Different damage mechanisms trigger elastic waves in the composite, with distinct AE signatures that closely follow the sequence of fracture mechanisms. AE monitoring is employed to capture signals associated with structural damage initiation and progression. The characteristic parameters of AE signals are correlated with crack modes and damage mechanisms. The evolution of AE parameters during the peak load transition is presented, which enables the timely AE detection of the maximum load transition. The combination of DIC and AE monitoring improves understanding of the mechanical response and failure mechanisms in cross-ply basalt fiber composites, offering valuable insights for possible performance monitoring and structural reliability in diverse engineering applications.