A Geometry Projection Method for the Optimal Design of Panel Reinforcements With Ribs Made of Plates

2016 ◽  
Author(s):  
Shanglong Zhang ◽  
Julián A. Norato
Keyword(s):  
Optimization Methods ◽  
Pressure Vessels ◽  
Density Field ◽  
Uniform Grid ◽  
Constant Thickness ◽  
Aircraft Wings ◽  
Ship Hulls ◽  
Gradient Based ◽  
Reinforcing Ribs ◽  
Reinforcement Design

The stiffness of plate structures can be significantly improved by adding reinforcing ribs. In this paper, we are in particular concerned with stiffening of panels using ribs made of constant-thickness plates that may be, for example, welded to the panel. These ribs are common in, for example, the reinforcement of ship hulls, aircraft wings, pressure vessels and storage tanks. Existing methods either produce rib designs that cannot be fabricated with plates, or employ heuristics that produce non-optimal designs. This paper presents a method for optimally designing the topology, locations and dimensions of rectangular ribs to reinforce a panel. To this end, we smoothly project an analytic, explicit geometry representation of a set of ribs onto a continuous density field over a design envelope. This density field is discretized in an element-wise manner on a uniform grid for analysis. The initial design consists of a prescribed set of ribs, constrained to remain perpendicular to the panel to facilitate manufacturing and joining of the ribs. The advantages of our method are two-fold. On one hand, as in classical density-based topology optimization, we circumvent re-meshing by using a fixed finite element grid for the analysis, and the differentiability of the projection allows us to employ efficient and robust gradient-based optimization methods. On the other hand, the explicit geometry representation provides a direct translation into CAD, it produces reinforcement designs that conform to available plate cutting and joining processes, and it allows us to impose a constraint on the minimum separation between any two ribs to guarantee clear gaps for weld gun access. Also, bounds on the ribs dimensions can be naturally and directly accommodated. We present numerical examples of our panel reinforcement design under different types of loadings to demonstrate the applicability of the proposed method.

Optimal Design of Panel Reinforcements With Ribs Made of Plates

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Shanglong Zhang ◽  
Julián A. Norato
Keyword(s):  
Computer Aided Design ◽  
Pressure Vessels ◽  
Constant Thickness ◽  
Plate Structures ◽  
Aircraft Wings ◽  
Ship Hulls ◽  
Plate Elements ◽  
Reinforcing Ribs ◽  
Aided Design ◽  
And Storage

The stiffness of plate structures can be significantly improved by adding reinforcing ribs. In this paper, we are concerned with the stiffening of panels using ribs made of constant-thickness plates. These ribs are common in, for example, the reinforcement of ship hulls, aircraft wings, pressure vessels, and storage tanks. Here, we present a method for optimally designing the locations and dimensions of rectangular ribs to reinforce a panel. The work presented here is an extension to our previous work to design structures made solely of discrete plate elements. The most important feature of our method is that the explicit geometry representation provides a direct translation to a computer-aided design (CAD) model, thereby producing reinforcement designs that conform to available plate cutting and joining processes. The main contributions of this paper are the introduction of two important design and manufacturing constraints for the optimal rib layout problem. One is a constraint on the minimum separation between any two ribs to guarantee adequate weld gun access. The other is a constraint that guarantees that ribs do not interfere with holes in the panel. These holes may be needed to, for example, route components or provide access, such as a manhole. We present numerical examples of our method under different types of loadings to demonstrate its applicability.

Stresses in Pressurized Circular Shells With Discontinuities, With or Without Stiffeners

1972 ◽  
Vol 16 (02) ◽  
pp. 140-147
Author(s):  
A. J. Durelli ◽  
V. J. Parks
Keyword(s):  
Experimental Determination ◽  
Mechanical Strain ◽  
Three Dimensional ◽  
Pressure Vessels ◽  
Circular Cylinders ◽  
Constant Thickness ◽  
Strain Gages ◽  
Circular Holes ◽  
Reinforcing Ribs

This paper is a summary of a series of five research programs dealing with the experimental determination of stresses, strains, and displacements in circular cylinders subjected to pressure. The vessels have either constant thickness or transverse reinforcing ribs. Circular holes, with either plain or reinforced edges, are located in different positions of the vessels. The methods used for the analysis are: brittle coatings, three-dimensional photoelasticity ("freezing" technique), and electrical and mechanical strain gages. The most important results are summarized in a table. These results will be of interest to designers of underwater ships and of pressure vessels in general.

An Adjoint Based Approach for Optimal Design of Morphing SMP

2013 ◽  
Author(s):  
Shuang Wang ◽  
John C. Brigham
Keyword(s):  
Shape Change ◽  
Mechanical Energy ◽  
Optimization Methods ◽  
Design Parameters ◽  
Optimization Strategy ◽  
Thermally Activated ◽  
Gradient Based ◽  
Nonlinear Optimization Methods ◽  
Numerical Representations ◽  
Objective Functional

This work presents a strategy to identify the optimal localized activation and actuation for a morphing thermally activated SMP structure or structural component to obtain a targeted shape change or set of shape features, subject to design objectives such as minimal total required energy and time. This strategy combines numerical representations of the SMP structure’s thermo-mechanical behavior subject to activation and actuation with gradient-based nonlinear optimization methods to solve the morphing inverse problem that includes minimizing cost functions which address thermal and mechanical energy, morphing time, and damage. In particular, the optimization strategy utilizes the adjoint method to efficiently compute the gradient of the objective functional(s) with respect to the design parameters for this coupled thermo-mechanical problem.

scholarly journals Benchmarking Adaptive Variational Quantum Eigensolvers

2020 ◽  
Vol 8 ◽  
Author(s):  
Daniel Claudino ◽  
Jerimiah Wright ◽  
Alexander J. McCaskey ◽  
Travis S. Humble
Keyword(s):  
Quantum State ◽  
Energy Eigenvalue ◽  
Molecular Size ◽  
Optimization Methods ◽  
Superior Performance ◽  
Prepared State ◽  
Gradient Based ◽  
Structure Problem ◽  
Relevant Finding ◽  
Electronic Ground

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

A Reinforcement Design Method Based on Analysis of Large Openings in Cylindrical Pressure Vessels

1996 ◽  
Vol 118 (4) ◽  
pp. 502-506 ◽  
Author(s):  
M. D. Xue ◽  
K. C. Hwang ◽  
W. Lu¨ ◽  
W. Chen
Keyword(s):  
Fourier Series ◽  
Present Method ◽  
Fourier Coefficients ◽  
Design Method ◽  
Large Diameter ◽  
Pressure Vessels ◽  
Diameter Ratio ◽  
Cylindrical Coordinates ◽  
Reinforcement Design ◽  
Good Agreement

The analytical solution is given for two orthogonally intersecting cylindrical shells with large diameter ratio d/D subjected to internal pressure. The modified Morley equation is used for the shell with cutout and the Love equation for the tube with nonplanar end. The continuity conditions of forces and displacements at the intersection are expressed in 3-D cylindrical coordinates (ρ, θ, z), and are expanded in Fourier series of θ. The Fourier coefficients are obtained by numerical quadrature. The present results are in good agreement with those obtained by tests and by FEM for ρ0 = d/D ≤ 0.8. The typical curves of SCF versus t/T and d/DT and reinforcement coefficients g, h versus D/T0 for each ρ0 are given on the present method.

Estimation of Thermal Boundary Conditions by Gradient Based and Genetic Algorythms

2012 ◽  
Vol 729 ◽  
pp. 144-149 ◽  
Author(s):  
Imre Felde
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Nsga Ii ◽  
Thermal Boundary Conditions ◽  
Treatment Processes ◽  
Gradient Based ◽  
Type Boundary

The prediction of third type boundary conditions occurring during heat treatment processes is an essential requirement for characterization of heat transfer phenomena. In this work, the performance of four optimization techniques is studied. These models are the Conjugate Gradient Method, the Levenberg-Marquardt Method, the Simplex method and the NSGA II algorithm. The models are used to estimate the heat transfer coefficient during transient heat transfer. The performance of the optimization methods is demonstrated using numerical techniques.

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