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Bo Wang - One of the best experts on this subject based on the ideXlab platform.

  • symplectic Superposition Method based new analytic bending solutions of cylindrical shell panels
    International Journal of Mechanical Sciences, 2019
    Co-Authors: Xinran Zheng, Yu Sun, Mingqi Huang, Bo Wang
    Abstract:

    Abstract Pursuing analytic bending solutions of cylindrical shell panels without two opposite simply supported edges is a classic but very difficult type of problems. The main challenge is on the mathematical complexity of the boundary value problems of the governing high-order partial differential equations. In this paper, the first endeavor is made on extending an up-to-date symplectic Superposition Method to bending of cylindrical panels, with focus on clamped panels and their variants. By introducing the problems into the Hamiltonian system (in physics) and the symplectic space (in mathematics), they come down to the symplectic eigen problems, which are analytically solved for fundamental analytic solutions of three types of subproblems, followed by Superposition for final solutions. The new analytic solutions for the panels with four different combinations of boundary conditions are obtained, with comprehensive results tabulated to serve as benchmarks for future studies, all of which are well validated by the finite element Method. The rigorous derivation by the present Method without any assumptions/prior knowledge of solution forms may provide an exceptional route to more analytic solutions of some intractable shell problems.

  • symplectic Superposition Method for new analytic buckling solutions of rectangular thin plates
    International Journal of Mechanical Sciences, 2016
    Co-Authors: Bo Wang
    Abstract:

    Abstract Buckling of the rectangular thin plates is a class of problems of fundamental importance in mechanical engineering. Although various theoretical and numerical approaches have been developed, benchmark analytic solutions are still rare due to the mathematical difficulty in solving the complex boundary value problems of the governing high-order partial differential equation. Actually, most available solutions can be categorized as either “accurate” for the plates with two opposite edges simply supported or “approximate” for those without two opposite edges simply supported. In this paper, we present the first work on the symplectic Superposition Method-based analytic buckling solutions of the rectangular thin plates. A Hamiltonian system-based variational principle via the Lagrangian multiplier Method is proposed to formulate the thin plate buckling in the symplectic space. Then the governing equation is analytically solved for some fundamental subproblems which are superposed to yield the final solutions of the original problems. For each problem, a set of equations are produced with respect to the expansion coefficients of the quantities imposed on the plate edges. The existence of the nontrivial solutions of the equations sets the requirement that the determinant of the coefficient matrix be zero, which leads to a transcendental equation with respect to the buckling loads. The buckling mode shapes are obtained by substituting the nontrivial coefficient solutions into the mode shape solutions of the subproblems, followed by Superposition. Four types of buckling problems are studied for the plates with combinations of clamped and simply supported edges, without two opposite edges simply supported. The developed Method as well as the accurate analytic results is well validated by the finite element Method and very few analytic results from the literature.

  • hamiltonian system based benchmark bending solutions of rectangular thin plates with a corner point supported
    International Journal of Mechanical Sciences, 2014
    Co-Authors: Bo Wang
    Abstract:

    The benchmark bending solutions of rectangular thin plates with a corner point‐supported are obtained by an up-to-date symplectic Superposition Method within the framework of the Hamiltonian system. The developed Method offers a rational way to obtain the solutions of corner point supported thin plates with sufficient accuracy. Appropriate extension of the Method can also yield more benchmark solutions of the similar problems. Comprehensive numerical results are presented for future validation of various approximate/numerical Methods.

Dimitrios Samios - One of the best experts on this subject based on the ideXlab platform.

Elton Luis Gasparotto Denardin - One of the best experts on this subject based on the ideXlab platform.

Paulo Roberto Janissek - One of the best experts on this subject based on the ideXlab platform.

Bhudatt R Paliwal - One of the best experts on this subject based on the ideXlab platform.

  • modeling dose distributions from portal dose images using the convolution Superposition Method
    Medical Physics, 1996
    Co-Authors: Todd Mcnutt, Rock T Mackie, P J Reckwerdt, Bhudatt R Paliwal
    Abstract:

    Post-treatment dose verification refers to the process of reconstructing delivered dose distributions internal to a patient from information obtained during the treatment. The exit dose is commonly used to describe the dose beyond the exit surface of the patient from a megavoltage photon beam. Portal imaging provides a Method of determining the dose in a plane distal to a patient from a megavoltage therapeutic beam. This exit dose enables reconstruction of the dose distribution from external beam radiation throughout the patient utilizing the convolution/Superposition Method and an extended phantom. An iterative convolution/Superposition algorithm has been created to reconstruct dose distributions in patients from exit dose measurements during a radiotherapy treatment. The Method is based on an extended phantom that includes the patient CT representation and an electronic portal imaging device (EPID). The convolution/Superposition Method computes the dose throughout the extended phantom, which allows the portal dose image to be predicted in the EPID. The process is then reversed to take the portal dose measurement and infer what the dose distribution must have been to produce the measured portal dose. The dose distribution is modeled without knowledge of the incident intensity distribution, and includes the effects of scatter in the computation. The iterative Method begins by assuming that the primary energy fluence (PEF) at the portal image plane is equal to the portal dose image, the PEF is then back-projected through the extended phantom and convolved with the dose deposition kernel to determine a new prediction of the portal dose image. The image of the ratio of the computed PEF to the computed portal dose is then multiplied by the measured portal dose image to produce a better representation of the PEF. Successive iterations of this process then converge to the exiting PEF image that would produce the measured portal dose image. Once convergence is established, the dose distribution is determined by back-projecting the PEF and convolving with the dose deposition kernel. The Method is accurate, provided the patient representation during treatment is known. The Method was used on three phantoms with a photon energy of 6 MV to verify convergence and accuracy of the algorithm. The reconstructed dose volumes agree to within 3% of the forward computation dose volumes. Furthermore, this technique assumes no prior knowledge of the incident fluence and therefore may better represent the dose actually delivered.

  • calculation of portal dose using the convolution Superposition Method
    Medical Physics, 1996
    Co-Authors: Todd Mcnutt, Rock T Mackie, P J Reckwerdt, Nikos Papanikolaou, Bhudatt R Paliwal
    Abstract:

    The convolution/Superposition Method was used to predict the dose throughout an extended volume, which includes a phantom and a portal imaging device. From the calculated dose volume, the dose delivered in the portal image plane was extracted and compared to a portal dose image. This comparison aids in verifying the beam configuration or patient setup after delivery of the radiation. The phantoms used to test the accuracy of this Method include a solid water cube, a Nuclear Associates CT phantom, and an Alderson Rando thorax phantom. The dose distribution in the image plane was measured with film and an electronic portal imaging device in each case. The calculated portal dose images were within 4% of the measured images for most voxels in the central portion of the field for all of the extended volumes. The convolution/Superposition Method also enables the determination of the scatter and primary dose contributions using the particular dose deposition kernels for each contribution. The ratio of primary dose to total dose was used to extract the primary dose from the detected portal image, which enhances the megavoltage portal images by removing scatter blurring. By also predicting the primary energy fluence, we can find the ratio of computed primary energy fluence to total dose. Multiplying this ratio by the measured dose image estimates the relative primary energy fluence at the portal imager. The image of primary energy fluence possesses higher contrast and may be used for further quantitative image processing and dose modeling.