Proportional Topology Optimization: A new non-gradient method for solving stress constrained and minimum compliance problems and its implementation in MATLAB

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-gradient method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing gradient optimality criteria method. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org.Comment: 18 pages, 8 figures, and 2 appendices (MATLAB codes

Multiresolution molecular mechanics: surface effects and iso-parametric analysis

Within the generalized framework of the newly presented energy-based concurrent atomistic/continuum method Multiresolution Molecular Mechanics (MMM) [1], two proposed summation rules, the bulk summation and the edge summation rule to efficiently determine the bulk and surface energy distribution respectively, consists the optimal MMM summation rule. In Ref. [1], the bulk summation rule has been verified and proved to outperform the widely used Gauss quadrature. In this study, the edge summation rule will be employed to specifically capture surface effects. This is achieved in three steps: (i) use the edge summation rule to determine the surface energy distribution for any given finite element method (FEM) shape function analytically; (ii) select the optimal number of surface primary sampling atoms on the surfaces, and (iii) determine the weight for each surface primary sampling atoms using the edge summation rule and then use their energies to sampling the surface energy. In particular, the effect of the selection of surface primary sampling atoms on the accuracy of capturing surface effect will be studied. In addition, the sampling errors introduced by employing the edge summation rule will be determined through error structure analysis. Then iso-parametric analysis within the generalized framework of MMM will be performed to standardize the implementation procedure of MMM, as is widely employed in conventional FEM. The iso-parametric analysis is achieved by performing the surface summation rule and the bulk summation rule within some specifically designed surface parent elements and bulk parent elements. In particular, the iso-parametric analysis will be performed with respect to linear, bilinear, and quadratic elements undergoing tensile, shear, and bending deformations and will be compared against full atomistic to show the effectiveness of MMM. REFERENCES [1] Yang, Q., To, A.C. Multiresolution molecular mechanics: a unified and consistent framework for general finite element shape functions. Comp. Meth. Appl. Mech. Eng. (under review). [2] Yang, Q., Biyikli, E., To, A.C. Multiresolution molecular mechanics: statics. Comp. Meth. Appl. Mechanics Eng. 2013, 258, 26‑38. [3] Yang, Q., Biyikli, E., To, A.C. Multiresolution molecular mechanics: convergence and error structure analysis. Comp. Meth. Appl. Mech. Eng. 2014, 269, 20‑45 . [4] Biyikli, E., Yang, Q., To, A.C. Multiresolution molecular mechanics: dynamics. Comp. Meth. Appl. Mech. Eng. 2014, 274, 42‑55

Lateral load capacity of drilled shafts in jointed rock

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1999.Includes bibliographical references (p. 263).Large vertical (axial) and lateral loads often act on the heads of drilled shafts in jointed rock. In current design practice, the p-y curve method used in design of laterally loaded drilled shafts in soil is adopted in the design of such shafts in jointed rock. The p-y curve method treats the soil as a continuum. The continuum model is not applicable to jointed rock, in which the joints form blocks. A new discontinuum model was developed in this thesis to determine the lateral load capacity of drilled shafts in a jointed rock mass with two and three joint sets. It contains two parts: a kinematic and a kinetic analysis. In the kinematic analysis, the removability theorem of a convex block is expanded to analyze the removability of a block intersecting a pile and the removability of a combination of blocks. Based on these removability theorems, a method was developed to select removable combinations of blocks using easily constructed 2-dimensional figures only. In kinetics, each selected removable combination of blocks is analyzed with the limit equilibrium approach to determine the ultimate lateral load capacity. Although the analysis is similar to slope stability analysis, it is more complicated with the addition of a lateral force exerted by the pile and the vertical pile load exerted on the wedge. The analysis also considers the weight of the wedge, the shearing resistance along the joints, and the vertical pile load exerted on the wedge. Simple analytical relations were developed to solve for the ultimate lateral load capacity.by Albert C. To.S.M

Survival Analysis of Re-resection Versus Radiofrequency Ablation for Intrahepatic Recurrence After Hepatectomy for Hepatocellular Carcinoma

Ó The Author(s) 2011. This article is published with open access at Springerlink.com Background Tumor recurrence after resection of hepatocellular carcinoma is a common phenomenon. Re-resection and radiofrequency ablation (RFA) are good options for treating recurrent HCC. This study compared the efficacy of these two modalities in the treatment of intrahepatic HCC recurrence after hepatectomy. Methods From January 2001 to December 2008, a total of 179 patients developed intrahepatic HCC recurrence after hepatectomy. To treat the recurrence, 29 patients underwent re-resection and 45 patients had RFA. Patient characteristics, clinicopathologic data, and survival outcomes were reviewed. Results Child-Pugh status, time to develop first recurrence (12.2 vs. 8.7 months), and recurrent tumor size (2.1 vs. 2.1 cm) were comparable for the two groups. Time to develop a second intrahepatic recurrence after re-resection and RFA was 5.9 and 4.0 months respectively. The 1-, 3-, and 5-year disease-free survival rates were 41.4%, 24.2%, and 24.2 % after re-resection and 32.2%, 12.4%, and 9.3% after RFA (p = 0.14). The 1-, 3-, and 5-year overall survival rates were 89.7%, 56.5%, and 35.2 % after re-resection and 83.7%, 43.1%, and 29.1 % after RFA (p = 0.48). For the second recurrence, 33.3 % of patients underwent a second round of RFA and 10.0 % underwent a third resection