Shape Optimization Of Beams Research Articles

Laser beam shape optimization in powder bed fusion of metals

Laser beam shape optimization in powder bed fusion of metals

Pseudospectral Approach to the Shape Optimization of Beams Under Buckling Constraints

In this article, a direct transcription approach to the minimization of the volume of elastic straight beams undergoing plane deformation and subject to buckling loads is presented. In particular, the so-called pseudospectral method is employed, where state variables are approximated by Lagrange interpolating polynomials and static equations are collocated at Legendre-Gauss-Radau nonuniform mesh points. The resulting shape optimization problems are thus transcribed into constrained nonlinear programming problems, which in turn are solved by developed routines. Historical benchmark and academic problems such as simply supported beams subject to a concentrated compressing force, compressed and rotating cantilever beams and simply supported beams under a non-conservative follower distributed load are revisited and numerically solved under the conditions of plane deformation theory. Numerical solutions are discussed and compared to those obtained by the shooting method, which is largely employed for these problems, emphasizing how the proposed method could forecast optimal cross sectional area distributions within a unified fashion and without resorting to accurate guesses beforehand.

Optimization of beam shaping and error quantification of calibration approach using E-FISHG based electric field measurements

Electric-field measurement based on the electric-field-induced second-harmonic generation (E-FISHG) method is a promising tool for a noncontact field measurement in plasmas and gases. For the E-FISHG method, a probing laser beam is focused at the measurement target by a lens, and the signals integrated along the laser path are acquired. Although the signal is frequently calibrated under uniform electric fields, the yielded value is erroneous if one does not consider the difference in the electric-field-profiles between the calibration and measurement. In this paper, we review the calibration and measurement targets of relevant studies, assess the error in the conventional method for the streamer discharge measurement, and give guidelines on which calibration approach to use depending on the electric field profile to be measured. Our approach uses cylindrical-to-cylindrical electrodes and multipoint measurement corresponding to the target length along the optical path, gas, and pressure.

Laser Beam Shape Optimization in Powder Bed Fusion of Metals

Laser Beam Shape Optimization in Powder Bed Fusion of Metals

Optimization of beam shaping for ultrasensitive inertial measurement using a phase-only spatial light modulator.

This study proposes an approach to generate a uniform flat-top beam with a liquid crystal spatial light modulator (LC-SLM) to optimize ultrasensitive inertial measurement. The random incomplete Gaussian beam is modulated into a flat-top beam by uploading a beam shaping optimization algorithm on an LC-SLM. Simulation results verify the effectiveness of the proposed method. The beam obtained from the experimental results with the 4f filter system optimization also conforms to the properties of the generated flat-top beam. Compared to existing beam shaping algorithms for simulation and experimental analysis, the beam shaping design based on the LC-SLM to optimize the ultrasensitive inertial measurement is realized. This method has also been verified to be effective in beam shaping in various beam situations. The application of this method in ultrahigh-sensitivity inertial measurement should prove significant.

Shaped beams: unlocking new geometry for efficient structures

Society is building at an unprecedented rate: to house over 200,000 people moving to cities each day building stock will need to double by 2060. Importantly, the embodied carbon of construction due to material extraction, manufacturing, transportation, and demolition accounts for 11% of global carbon emissions, and this number is only expected to rise. With no end to construction in sight, it is essential that we develop better building practices. The research presented in this paper begins with the critical issue of embodied energy in horizontal structural systems. In high-rise buildings, between 60 and 80% of the mass and embodied energy of the structure can be found in the floors, suggesting a compelling starting point for materially efficient design. A reduction in a floor system’s mass can lead to a similar reduction in the mass of vertical (columns, walls) and lateral systems. This paper focuses on the design of horizontal spanning elements, such as floor beams and slabs, and has two parts. The first part evaluates and compares historic methods of shaped beam design and classical methods of structural optimization. The second part presents a new flexible method of beam shape optimization. These design methods for structural efficiency allow us to build far more with far less, reducing the environmental and economic costs of construction while meeting the demands of a growing population.

Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures

Straight beams, rods and trusses are common elements in structural and mechanical engineering, but recent advances in additive manufacturing now also enable efficient freeform fabrication of curved, deformable beams and beam structures, such as microstructures, metamaterials and conformal lattices. To exploit this new design freedom for applications with nonlinear mechanical behavior, we introduce an isogeometric method for shape optimization of curved 3D beams and beam structures. The geometrically exact Cosserat rod theory is used to model nonlinear 3D beams subject to large deformations and rotations. The initial and current geometry are parameterized in terms of NURBS curves describing the beam centerline and an isogeometric collocation approach is used to discretize the strong form of the balance equations. Then, a nonlinear optimization problem is formulated in order to optimize the positions of the control points of the NURBS curve that describes the beam centerline, i.e., the geometry or shape of the beam. To solve the design problem using gradient-based algorithms, we introduce semi-analytical, inconsistent analytical and fully analytical approaches for calculation of design sensitivities. The methods are numerically validated and their performance is investigated, before the applicability and versatility of our 3D beam shape optimization method is illustrated in various numerical applications, including optimization of an auxetic 3D metamaterial.

Into the development of a model to assess beam shaping and polarization control effects on laser cutting

This paper offers an in-depth look into beam shaping and polarization control as two of the most promising techniques for improving industrial laser cutting of metal sheets. An assessment model is developed for the study of such effects. It is built upon several modifications to models as available in literature in order to evaluate the potential of a wide range of considered concepts. This includes different kinds of beam shaping (achieved by extra-cavity optical elements or asymmetric diode staking) and polarization control techniques (linear, cross, radial, azimuthal). A fully mathematical description and solution procedure are provided. Three case studies for direct diode lasers follow, containing both experimental data and parametric studies. In the first case study, linear polarization is analyzed for any given angle between the cutting direction and the electrical field. In the second case several polarization strategies are compared for similar cut conditions, evaluating, for example, the minimum number of spatial divisions of a segmented polarized laser beam to achieve a target performance. A novel strategy, based on a 12-division linear-to-radial polarization converter with an axis misalignment and capable of improving cutting efficiency with more than 60%, is proposed. The last case study reveals different insights in beam shaping techniques, with an example of a beam shape optimization path for a 30% improvement in cutting efficiency. The proposed techniques are not limited to this type of laser source, neither is the model dedicated to these specific case studies. Limitations of the model and opportunities are further discussed.

Speckle-based at-wavelength metrology of X-ray mirrors with super accuracy

X-ray active mirrors, such as bimorph and mechanically bendable mirrors, are increasingly being used on beamlines at modern synchrotron source facilities to generate either focused or "tophat" beams. As well as optical tests in the metrology lab, it is becoming increasingly important to optimise and characterise active optics under actual beamline operating conditions. Recently developed X-ray speckle-based at-wavelength metrology technique has shown great potential. The technique has been established and further developed at the Diamond Light Source and is increasingly being used to optimise active mirrors. Details of the X-ray speckle-based at-wavelength metrology technique and an example of its applicability in characterising and optimising a micro-focusing bimorph X-ray mirror are presented. Importantly, an unprecedented angular sensitivity in the range of two nanoradians for measuring the slope error of an optical surface has been demonstrated. Such a super precision metrology technique will be beneficial to the manufacturers of polished mirrors and also in optimization of beam shaping during experiments.

Advanced in situ metrology for x-ray beam shaping with super precision

We report a novel method for in situ metrology of an X-ray bimorph mirror by using the speckle scanning technique. Both the focusing beam and the "tophat" defocussed beam have been generated by optimizing the bimorph mirror in a single iteration. Importantly, we have demonstrated that the angular sensitivity for measuring the slope error of an optical surface can reach accuracy in the range of two nanoradians. When compared with conventional ex-situ metrology techniques, the method enables a substantial increase of around two orders of magnitude in the angular sensitivity and opens the way to a previously inaccessible region of slope error measurement. Such a super precision metrology technique will be beneficial for both the manufacture of polished mirrors and the optimization of beam shaping.

SU‐E‐T‐521: Feasibility Study of a Rotational Step‐And‐Shoot IMRT Treatment Planning Approach

Purpose:Rotational step‐and‐shot IMRT (r‐IMRT) could improve delivery efficiency with good dose conformity, especially if it can leverage the burst mode of the accelerator where radiation is turned on/off momentarily while the gantry rotates continuously. The challenge for the r‐IMRT planning is to minimize the number of beams to achieve a fast and smooth rotational delivery.Methods:Treatment plans for r‐IMRT were created using an in‐house treatment planning system. To generate the plan using a very few beams, gantry angle was optimized by weighting the beam monitoring unit (MU), and beam shape optimization was a combination of column search with k‐means clustering. A prostate case and a head and neck case were planned using r‐IMRT. The dosimetry is compared to s‐IMRT planned with Varian Eclipse treatment planning system.Results:With the same PTV dose coverage D95=100%, the r‐IMRT plans shows comparable sparing as the s‐IMRT plans in the prostate for the rectum D10cc and the bladder Dmean, and in the head and neck for the spinal cord Dmax, the brain stem Dmax, the left/right parotid Dmean, the larynx Dmean, and the mandible Dmean. Both plans meet the established institutional clinical dosimetric criteria. The r‐IMRT plan uses 19 beam/405 MU for the prostate, and 68 beam/880 MU for the head and neck, while the s‐IMRT uses 7 beam/724 MU and 9 beam/1812 MU, respectively. Compared to the corresponding s‐IMRT, r‐IMRT has a reduction of MUs of 44% for the prostate case and 41% for the head and neck case.Conclusions:We have demonstrated the feasibility of a rotational step & shoot IMRT treatment planning approach that significantly shortens the conventional IMRT treatment beam‐on time without degrading the dose comformity.

Modeling and Analysis of a Piezoelectric Energy Harvester with Varying Cross-Sectional Area

This paper reports on the modeling and on the experimental verification of electromechanically coupled beams with varying cross-sectional area for piezoelectric energy harvesting. The governing equations are formulated using the Rayleigh-Ritz method and Euler-Bernoulli assumptions. A load resistance is considered in the electrical domain for the estimate of the electric power output of each geometric configuration. The model is first verified against the analytical results for a rectangular bimorph with tip mass reported in the literature. The experimental verification of the model is also reported for a tapered bimorph cantilever with tip mass. The effects of varying cross-sectional area and tip mass on the electromechanical behavior of piezoelectric energy harvesters are also discussed. An issue related to the estimation of the optimal load resistance (that gives the maximum power output) on beam shape optimization problems is also discussed.

Shape optimization of beam due to lateral buckling problem

Based on a non-linear mathematical model of lateral buckling of a slender beam with a narrow rectangular cross section, the variational formulation of the two-parametric optimization problem is given in the dimensionless form. An optimal shape is obtained by solving the variational problem using the Rayleigh–Ritz method with the orthogonal system of trigonometric functions. By a partial solution of the Euler–Lagrange differential equation of the variational problem, a proof is given that in the case of the optimal shape, a maximal reference stress according to the total strain energy theory is constant along the beam. An example of extrapolation of the two-parametric optimization problem solution is represented.

Beam Shape Optimization for Power Harvesting

A problem in piezoelectric bimorph energy harvesting is to generate the most power with limits in system mass. The authors propose a new approach: to change the shape of the beam to concentrate the strain in sections of the beam where it can contribute the most to transduction. A vibration model of beams with non-uniform width is developed and validated with shaker table tests. Three beams with different shapes are tested over a wide band, encompassing the lowest two modes of vibration. An optimal beam shape is calculated using a heuristic optimization code and the attributes of this optimal beam are discussed. Then, beam shapes are optimized to allow for increased base excitation and constrained by maximum root strain. Finally, the tip mass-to-beam mass ratio is studied parametrically, correlating increased transduction with increased beam mass.

Performance of the evolutionary structural optimization-based approaches with different criteria in the shape optimization of beams

This paper deals with the convergence of the Evolutionary Structural Optimization (ESO) and the Morphing ESO (MESO) solutions to the optimum in typical beam design problems. The ESO-based methods are very simple to implement via a computer code. Up to now, the ESO-based methods have been successfully applied for some structural optimization problems. There has not been presented any mathematical proof for the validity of the ESO-based methods yet. On the other hand, there are only a few optimization problems with exact analytical solutions for verifying the results of these methods. In this work, optimum shape of constant volume beams are obtained. It is shown that using different criteria, the optimum shapes obtained by the ESO and the MESO methods converge to the optimum.

Shape optimization of steel reinforced concrete beams

Steel reinforced concrete is perhaps the most versatile and widely used construction material. The versatility is attributed to mouldability of concrete to any conceivable shape. The inherent property of cracking of concrete is the reason for its low tensile strength and hence the design approach of RCC sections in flexure adopts the cracked section theory where in concrete in tension zone is ignored. Means, modes and methods of exploitation of concrete strength by conceiving shapes other than rectangular whereby ineffective concrete in tension zone is reduced and incorporated in compression zone where it is effective needs consideration. Shape optimization of beams is attempted in this analytical investigation employing Sequential Unconstrained Minimization Technique (SUMT). The results clearly show that trapezoidal beams happen to be less costlier than their rectangular counterparts, their usage needs serious reconsideration by the designers.