A discrete material optimization method with a patch strategy based on stiffness matrix interpolation

Pengwen Sun,Jie Zhang,Penghui Wu,Jiandong Li,Lanting Zhang,Weifei Hu 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.2

A discrete material optimization method with a patch strategy based on the stiffness matrix interpolation is proposed, and a comprehensive technical process of patch discrete material optimization using existing finite element software was developed. This method employs the stiffness matrix instead of the constitutive matrix for material interpolation, which facilitates the optimization process integrated with the existing finite element software. The element stiffness matrix can be derived directly from the finite element analysis, which can not only ensure the correctness of the data, but also reduce the programming work of solving the numerical integration of the composite constitutive matrix. The mathematical model of the patch discrete material optimization is established, which takes the artificial density as the design variable, the minimum compliance as the objective function, and the sequential quadratic programming (SQP) algorithm as the optimization solver. Numerical examples show that by seeking a balance between the number of regions and practical production, the performance of the composite could be further improved using the discrete material optimization method with a patch strategy. Besides, the convergence rate of the optimization is increased by introducing the sum constraints of the design variables and the value functions. The effectiveness and the feasibility of the method were verified.

Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation

Suchart Limkatanyu,Kittisak Kuntiyawichai,Enrico Spacone,권민호 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.42 No.1

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called “natural” element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation

Limkatanyu, Suchart,Kuntiyawichai, Kittisak,Spacone, Enrico,Kwon, Minho Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.42 No.1

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called "natural" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

Volume Adaptation Controls Stem Cell Mechanotransduction

Major, Luke G.,Holle, Andrew W.,Young, Jennifer L.,Hepburn, Matt S.,Jeong, Kwanghee,Chin, Ian L.,Sanderson, Rowan W.,Jeong, Ji Hoon,Aman, Zachary M.,Kennedy, Brendan F.,Hwang, Yongsung,Han, Dong-Wook American Chemical Society 2019 ACS APPLIED MATERIALS & INTERFACES Vol.11 No.49

<P>Recent studies have found discordant mechanosensitive outcomes when comparing 2D and 3D, highlighting the need for tools to study mechanotransduction in 3D across a wide spectrum of stiffness. A gelatin methacryloyl (GelMA) hydrogel with a continuous stiffness gradient ranging from 5 to 38 kPa was developed to recapitulate physiological stiffness conditions. Adipose-derived stem cells (ASCs) were encapsulated in this hydrogel, and their morphological characteristics and expression of both mechanosensitive proteins (Lamin A, YAP, and MRTFa) and differentiation markers (PPARγ and RUNX2) were analyzed. Low-stiffness regions (∼8 kPa) permitted increased cellular and nuclear volume and enhanced mechanosensitive protein localization in the nucleus. This trend was reversed in high stiffness regions (∼30 kPa), where decreased cellular and nuclear volumes and reduced mechanosensitive protein nuclear localization were observed. Interestingly, cells in soft regions exhibited enhanced osteogenic RUNX2 expression, while those in stiff regions upregulated the adipogenic regulator PPARγ, suggesting that volume, not substrate stiffness, is sufficient to drive 3D stem cell differentiation. Inhibition of myosin II (Blebbistatin) and ROCK (Y-27632), both key drivers of actomyosin contractility, resulted in reduced cell volume, especially in low-stiffness regions, causing a decorrelation between volume expansion and mechanosensitive protein localization. Constitutively active and inactive forms of the canonical downstream mechanotransduction effector TAZ were stably transfected into ASCs. Activated TAZ resulted in higher cellular volume despite increasing stiffness and a consistent, stiffness-independent translocation of YAP and MRTFa into the nucleus. Thus, volume adaptation as a function of 3D matrix stiffness can control stem cell mechanotransduction and differentiation.</P> [FIG OMISSION]</BR>

A simple method of stiffness matrix formulation based on single element test

Mau, S.T. Techno-Press 1999 Structural Engineering and Mechanics, An Int'l Jou Vol.7 No.2

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

配管系의 振動解析을 위한 周波數從屬 要素行列

梁保錫(B. S. Yang),安永供(Y. K. Ahn),崔沅鎬(W. H. Choi) 한국해양공학회 1992 韓國海洋工學會誌 Vol.6 No.2

This paper presents an approach for the derivation of frequency-dependent element matrices for vibration analysis of piping systems containing a moving medium. The dynamic stiffness matrix is deduced from transfer matrix, and, in turn, the frequency-dependent element matrices are derived. Numerical examples show that this method gives more accurate results than those obtained using the conventional static shape function based element matrices.

Matrix cross-linking–mediated mechanotransduction promotes posttraumatic osteoarthritis

Kim, Jin-Hong,Lee, Gyuseok,Won, Yoonkyung,Lee, Minju,Kwak, Ji-Sun,Chun, Churl-Hong,Chun, Jang-Soo National Academy of Sciences 2015 PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF Vol.112 No.30

<P>Osteoarthritis (OA) is characterized by impairment of the load-bearing function of articular cartilage. OA cartilage matrix undergoes extensive biophysical remodeling characterized by decreased compliance. In this study, we elucidate the mechanistic origin of matrix remodeling and the downstream mechanotransduction pathway and further demonstrate an active role of this mechanism in OA pathogenesis. Aging and mechanical stress, the two major risk factors of OA, promote cartilage matrix stiffening through the accumulation of advanced glycation end-products and up-regulation of the collagen cross-linking enzyme lysyl oxidase, respectively. Increasing matrix stiffness substantially disrupts the homeostatic balance between chondrocyte catabolism and anabolism via the Rho-Rho kinase-myosin light chain axis, consequently eliciting OA pathogenesis in mice. Experimental enhancement of nonenzymatic or enzymatic matrix cross-linking augments surgically induced OA pathogenesis in mice, and suppressing these events effectively inhibits OA with concomitant modulation of matrix degrading enzymes. Based on these findings, we propose a central role of matrix-mediated mechanotransduction in OA pathogenesis.</P>

Matrix stiffness-modulated proliferation and secretory function of the airway smooth muscle cells.

Shkumatov, Artem,Thompson, Michael,Choi, Kyoung M,Sicard, Delphine,Baek, Kwanghyun,Kim, Dong Hyun,Tschumperlin, Daniel J,Prakash, Y S,Kong, Hyunjoon American Physiological Society 2015 American journal of physiology. Lung cellular and Vol.308 No.11

<P>Multiple pulmonary conditions are characterized by an abnormal misbalance between various tissue components, for example, an increase in the fibrous connective tissue and loss/increase in extracellular matrix proteins (ECM). Such tissue remodeling may adversely impact physiological function of airway smooth muscle cells (ASMCs) responsible for contraction of airways and release of a variety of bioactive molecules. However, few efforts have been made to understand the potentially significant impact of tissue remodeling on ASMCs. Therefore, this study reports how ASMCs respond to a change in mechanical stiffness of a matrix, to which ASMCs adhere because mechanical stiffness of the remodeled airways is often different from the physiological stiffness. Accordingly, using atomic force microscopy (AFM) measurements, we found that the elastic modulus of the mouse bronchus has an arithmetic mean of 23.1 ± 14 kPa (SD) (median 18.6 kPa). By culturing ASMCs on collagen-conjugated polyacrylamide hydrogels with controlled elastic moduli, we found that gels designed to be softer than average airway tissue significantly increased cellular secretion of vascular endothelial growth factor (VEGF). Conversely, gels stiffer than average airways stimulated cell proliferation, while reducing VEGF secretion and agonist-induced calcium responses of ASMCs. These dependencies of cellular activities on elastic modulus of the gel were correlated with changes in the expression of integrin-관1 and integrin-linked kinase (ILK). Overall, the results of this study demonstrate that changes in matrix mechanics alter cell proliferation, calcium signaling, and proangiogenic functions in ASMCs.</P>

Engineered Phage Matrix Stiffness-Modulating Osteogenic Differentiation

Lee, Hee-Sook,Kang, Jeong-In,Chung, Woo-Jae,Lee, Do Hoon,Lee, Byung Yang,Lee, Seung-Wuk,Yoo, So Young American Chemical Society 2018 ACS APPLIED MATERIALS & INTERFACES Vol.10 No.5

<P>Herein, we demonstrate an engineered phage mediated rmatrix for osteogenic differentiation with controlled stiffness by cross-linking the engineered, phage displaying Arg-Gly-Asp (RGD) and His-Pro-Gln (HPQ) with various Concentrations of streptavidin or polymer, poly(diallyldirnethylammonium)chltiride (PDDA). Osteogenic gene expressions showed that they were specifically increased when MC3T3 cells were cultured, on the stiffer phage matrix than the softer one. Our phage matrixes can be easily functionalized using chernical/gerietic engineering and-Used as a stem cell tissue matrix stiffness platform for modulating differential cell expansion and differentiation.</P>

Structural matrices of a curved-beam element

F.N. Gimena,P. Gonzaga,L. Gimena 국제구조공학회 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.33 No.2

This article presents the differential system that governs the mechanical behaviour of a curved-beam element, with varying cross-section area, subjected to generalized load. This system is solved by an exact procedure or by the application of a new numerical recurrence scheme relating the internal forces and displacements at the two end-points of an increase in its centroid-line. This solution has a transfer matrix structure. Both the stiffness matrix and the equivalent load vector are obtained arranging the transfer matrix. New structural matrices have been defined, which permit to determine directly the unknown values of internal forces and displacements at the two supported ends of the curved-beam element. Examples are included for verification.