Tatizo linalolengwaKatika shape optimization, design inaweza kudhibitiwa na radius ya tundu, nafasi ya notch, chamfer au boundary motion. Katika topology optimization, pseudo-density ya elementi, level-set field au topological sensitivity huamua wapi material ibaki na kama connectivity ibadilike. Ingawa representation hizi ni tofauti, zote hutumia mnyororo wa msingi: geometry → discretization → state solve → objective/constraint evaluation → sensitivity → regularization/filter → design update.Usanifu wa object-orientedSTORX hutenganisha brep2d, gridMesher, fea2d, simulation2d, functional, mfgConstraints, parameterOpt2d, density2d, levelset2d, evolutionary2d na pareto2d. Functional mpya huhitaji hasa evaluate na gradient; manufacturing constraint mpya hutumia filterDesign na filterSensitivity.B-Rep na FEABoundary Representation ya 2D hutumia vertices pamoja na line/arc segments kuunda domains zisizolazimika kuwa rectangular. Hii inaruhusu loads, supports na retained regions kufungamanishwa na boundaries za maana za jiometri.$$ R_{\mathrm{el}}(d)=K_{\mathrm{el}}d-f_{\mathrm{el}}=0. \tag{1} $$Kwa mfano wa gripper: karibu elementi 4,000, $E=2$ GPa, $\nu=0.35$, nguvu 10 N. Triangular FEA inatoa $1.00\times10^{-6}$ m na 6.87 MPa; grid FEA inatoa $1.05\times10^{-6}$ m na 6.31 MPa.Parametric shape optimization$$ \begin{aligned} \min_{p=[a,b,c,r]^\top}\;&C(d;p) \tag{2a}\ K_{el}(p)d-f_{el}&=0 \tag{2b}\ A-A_{\max}&\le0 \tag{2c}\ a_{\min}\le a&\le a_{\max} \tag{2d}\ b_{\min}\le b&\le b_{\max} \tag{2e}\ c_{\min}\le c&\le c_{\max} \tag{2f}\ r_{\min}\le r&\le r_{\max}. \tag{2g} \end{aligned} $$$$ C_i'=f^\top u_i' \tag{3} $$$$ K^{(k)}u_i'=-K_i'u^{(k)} \tag{4} $$$$ K_i'= \frac{K^{(k)}_{i,\mathrm{pert}}-K^{(k)}}{\Delta p_i}. \tag{5} $$Semi-analytic FD: $p_0=(0.20,0.15,1.20,0.10)$ hadi $p_{FD}=(0.363,0.224,1.500,0.076)$; iterations 118, FEA runs 1,070; area 1.906→1.7995 m²; compliance 3.91→3.95 N·m; maximum deflection karibu 0.04 mm.GlobalSearch: $p_{GS}=(0.310,0.226,1.248,0.141)$, area 1.79 m², compliance 4.022 N·m, FEA 305. MultiStart: $p_{MS}=(0.327,0.138,1.466,0.155)$, area 1.798 m², compliance 4.001 N·m, FEA 2,545. Random Search: $p_{RS}=(0.359,0.150,1.337,0.150)$, area 1.779 m², compliance 4.021 N·m, FEA 22.Level-set shape optimization$$ \psi(x) \begin{cases} 0,&x\notin\Omega\cup\partial\Omega \end{cases} \tag{6} $$$$ \begin{aligned} \min_\psi\;&\phi(\psi)\ |\Omega(\psi)|-V^*&\le0,\ R_{el}(d)&=0. \end{aligned} \tag{7} $$$$ \frac{\partial\psi}{\partial t} +\operatorname{sign}(\psi_0)(|\nabla\psi|-1)=0 \tag{8} $$$$ \operatorname{sign}(\psi) = \frac{\psi}{\sqrt{\psi^2+|\nabla\psi|^2\epsilon^2}}. \tag{9} $$Reinitialization hurejesha field karibu na signed-distance function ili $|\nabla\psi|\approx1$ bila kubadilisha zero-level-set.Density-based topology optimization$$ \begin{aligned} \min_\rho\;&\phi(d;\rho) \tag{10a}\ \sum_e\rho_ev_e-V^*&\le0 \tag{10b}\ K_{el}(\rho)d-f_{el}&=0 \tag{10c}\ 0\tau\} \tag{22} $$$$ \Omega_{\tau^-}^{keep} =\{p\in\Omega\mid\alpha(p)\tau^-\} \tag{23} $$$$ \Omega_{\tau^+}^{add} =\{p\in\Omega\mid\alpha(p)\tau^+\} \tag{24} $$$$ \begin{aligned} \min_{\Omega(x)\subseteq D}\;&\{V,\phi(d)\}\ V(x)&\le V^*,\ R_{el}(d)&=0. \end{aligned} \tag{25} $$$$ \Delta V(\Omega_1,\Omega_2) = V(\Omega_1\setminus\Omega_2) + V(\Omega_2\setminus\Omega_1) \le\delta. \tag{26} $$ESO huondoa material bila kuirudisha. BESO inaruhusu removal na re-introduction. PareTO inalenga local Pareto optimality kwa volume levels zinazofuatana na hutumia fixed-point iteration katika kila outer step.Minimum feature size na physical-density projection$$ \chi_e= \begin{cases} 1,&e\in\Omega_{design}\ 0,&\text{vinginevyo} \end{cases} \tag{27} $$$$ \tilde\rho_e= \frac{\sum_iH_{ei}\chi_i\rho_i} {\sum_iH_{ei}\chi_i} \tag{28} $$$$ H_{ei}= \begin{cases} r_{\min}-dist(e,i),&dist(e,i)\le r_{\min}\ 0,&\text{vinginevyo} \end{cases} \tag{29} $$$$ \frac{\partial\phi}{\partial\rho_i} = \sum_e \frac{\partial\phi}{\partial\tilde\rho_e} \frac{\partial\tilde\rho_e}{\partial\rho_i} \tag{30} $$$$ \frac{\partial\tilde\rho_e}{\partial\rho_i} = \frac{H_{ei}\chi_i}{\sum_jH_{ej}\chi_j} \tag{31} $$$$ \widehat{\left(\frac{\partial\phi}{\partial\rho_i}\right)} = \frac1{\max(\rho_i,\epsilon)} \sum_eH_{ei}\rho_i \frac{\partial\phi}{\partial\tilde\rho_e}, \quad\epsilon=10^{-3} \tag{32} $$$$ \hat\rho_e= \frac{\tanh(\beta\eta)+\tanh[\beta(\rho_e-\eta)]} {\tanh(\beta\eta)+\tanh[\beta(1-\eta)]} \tag{33} $$$$ \frac{\partial\hat\rho_e}{\partial\rho_e} = \frac{\beta[1-\tanh^2(\beta(\rho_e-\eta))]} {\tanh(\beta\eta)+\tanh[\beta(1-\eta)]} \tag{34} $$$$ \frac{\partial\phi}{\partial\rho_e} = \frac{\partial\phi}{\partial\hat\rho_e} \frac{\partial\hat\rho_e}{\partial\rho_e} \tag{35} $$$$ \frac{\partial\phi}{\partial\rho_i} = \sum_e \frac{\partial\phi}{\partial\hat\rho_e} \frac{\partial\hat\rho_e}{\partial\tilde\rho_e} \frac{\partial\tilde\rho_e}{\partial\rho_i}. \tag{36} $$Filter ya minimum feature size hupunguza checkerboard na thin members. Heaviside projection huongeza ukali wa mabadiliko ya material; katika chanzo $\eta=0.5$ na mifano ya $\beta=1,8,64$ inaonyeshwa.Retained regions$$ \rho_e^{filtered}=1 \quad\text{ikiwa}\quad\chi_e^{ret}=1 \tag{37} $$$$ \left.\frac{\partial\phi}{\partial\rho_e}\right|_{\chi_e^{ret}=1} = \min_i\left(\frac{\partial\phi}{\partial\rho_i}\right) \tag{38} $$$$ \left.\frac{\partial\phi}{\partial\phi_e}\right|_{\chi_e^{ret}=1}=0 \tag{39} $$$$ \left.\frac{\partial\phi}{\partial\rho_e}\right|_{\chi_e^{ret}=1} = \max_i\left(\frac{\partial\phi}{\partial\rho_i}\right). \tag{40} $$Gripper yenye elementi 10,000, PETG $E=2$ GPa, $\nu=0.35$, force 10 N na volume fraction 0.65: bila retain $C/C_0=0.32$; kwa circular regions retained $C/C_0=0.33$.Multiple loads, self-weight na heat conduction$$ C_{avg} = \frac1{N_L} \sum_{\ell=1}^{N_L}F^{(\ell)T}d^{(\ell)} \tag{41} $$Cantilever yenye elementi 3,200, $E=100$ GPa, $\nu=0.3$, volume fraction 0.5; loads ni $F_1=+200$ kN na $F_2=-100$ kN. Average compliance: LSSO 2.11, standard HJE 1.84, modified HJE 1.68, SIMP 1.89, PareTO 1.70 N·m.$$ \begin{aligned} \min_\rho\;&\phi(d;\rho) \tag{42a}\ \sum_e\rho_ev_e-V^*&\le0 \tag{42b}\ K_{el}(\rho)d-f_{el}-b(\rho)&=0 \tag{42c}\ 0

Question

Tatizo linalolengwaKatika shape optimization, design inaweza kudhibitiwa na radius ya tundu, nafasi ya notch, chamfer au boundary motion. Katika topology optimization, pseudo-density ya elementi, level-set field au topological sensitivity huamua wapi material ibaki na kama connectivity ibadilike. Ingawa representation hizi ni tofauti, zote hutumia mnyororo wa msingi: geometry → discretization → state solve → objective/constraint evaluation → sensitivity → regularization/filter → design update.Usanifu wa object-orientedSTORX hutenganisha brep2d, gridMesher, fea2d, simulation2d, functional, mfgConstraints, parameterOpt2d, density2d, levelset2d, evolutionary2d na pareto2d. Functional mpya huhitaji hasa evaluate na gradient; manufacturing constraint mpya hutumia filterDesign na filterSensitivity.B-Rep na FEABoundary Representation ya 2D hutumia vertices pamoja na line/arc segments kuunda domains zisizolazimika kuwa rectangular. Hii inaruhusu loads, supports na retained regions kufungamanishwa na boundaries za maana za jiometri.$$ R_{\mathrm{el}}(d)=K_{\mathrm{el}}d-f_{\mathrm{el}}=0. \tag{1} $$Kwa mfano wa gripper: karibu elementi 4,000, $E=2$ GPa, $\nu=0.35$, nguvu 10 N. Triangular FEA inatoa $1.00\times10^{-6}$ m na 6.87 MPa; grid FEA inatoa $1.05\times10^{-6}$ m na 6.31 MPa.Parametric shape optimization$$ \begin{aligned} \min_{p=[a,b,c,r]^\top}\;&C(d;p) \tag{2a}\ K_{el}(p)d-f_{el}&=0 \tag{2b}\ A-A_{\max}&\le0 \tag{2c}\ a_{\min}\le a&\le a_{\max} \tag{2d}\ b_{\min}\le b&\le b_{\max} \tag{2e}\ c_{\min}\le c&\le c_{\max} \tag{2f}\ r_{\min}\le r&\le r_{\max}. \tag{2g} \end{aligned} $$$$ C_i'=f^\top u_i' \tag{3} $$$$ K^{(k)}u_i'=-K_i'u^{(k)} \tag{4} $$$$ K_i'= \frac{K^{(k)}_{i,\mathrm{pert}}-K^{(k)}}{\Delta p_i}. \tag{5} $$Semi-analytic FD: $p_0=(0.20,0.15,1.20,0.10)$ hadi $p_{FD}=(0.363,0.224,1.500,0.076)$; iterations 118, FEA runs 1,070; area 1.906→1.7995 m²; compliance 3.91→3.95 N·m; maximum deflection karibu 0.04 mm.GlobalSearch: $p_{GS}=(0.310,0.226,1.248,0.141)$, area 1.79 m², compliance 4.022 N·m, FEA 305. MultiStart: $p_{MS}=(0.327,0.138,1.466,0.155)$, area 1.798 m², compliance 4.001 N·m, FEA 2,545. Random Search: $p_{RS}=(0.359,0.150,1.337,0.150)$, area 1.779 m², compliance 4.021 N·m, FEA 22.Level-set shape optimization$$ \psi(x) \begin{cases} <0,&x\in\Omega\ =0,&x\in\partial\Omega\ >0,&x\notin\Omega\cup\partial\Omega \end{cases} \tag{6} $$$$ \begin{aligned} \min_\psi\;&\phi(\psi)\ |\Omega(\psi)|-V^*&\le0,\ R_{el}(d)&=0. \end{aligned} \tag{7} $$$$ \frac{\partial\psi}{\partial t} +\operatorname{sign}(\psi_0)(|\nabla\psi|-1)=0 \tag{8} $$$$ \operatorname{sign}(\psi) = \frac{\psi}{\sqrt{\psi^2+|\nabla\psi|^2\epsilon^2}}. \tag{9} $$Reinitialization hurejesha field karibu na signed-distance function ili $|\nabla\psi|\approx1$ bila kubadilisha zero-level-set.Density-based topology optimization$$ \begin{aligned} \min_\rho\;&\phi(d;\rho) \tag{10a}\ \sum_e\rho_ev_e-V^*&\le0 \tag{10b}\ K_{el}(\rho)d-f_{el}&=0 \tag{10c}\ 0<\rho_{\min}\le\rho_e&\le1. \tag{10d} \end{aligned} $$$$ K=\sum_{\mathrm{assemble}}k_e(\rho_e) \tag{11} $$$$ C=d^\top Kd=\sum_e\rho_e^p d_e^\top K_0d_e \tag{12} $$$$ D_\rho C=-d^\top K'd \tag{13} $$$$ E(\rho_e)=\rho_e^pE_0 \tag{14} $$$$ \frac{\partial k_e}{\partial\rho_e} =p\rho_e^{p-1}k_0 \tag{15} $$$$ E(\rho_e)= \frac{\rho_e}{1+q(1-\rho_e)}E_0 \tag{16} $$$$ \frac{\partial k_e}{\partial\rho_e} = \frac{1+q}{[1+q(1-\rho_e)]^2}k_0. \tag{17} $$Framework inaruhusu SIMP au RAMP pamoja na OC, MMA au GCMMA. Continuation ya penalty inaweza kutumiwa kusukuma intermediate densities kuelekea solid/void.Level-set TO na topological sensitivity$$ \psi(x,y)=\mathbf1_D(x,y) \cos\left(\frac{n_x\pi x}{l_x}\right) \cos\left(\frac{n_y\pi y}{l_y}\right) \tag{18} $$$$ T(p)= \lim_{\epsilon\to0^+} \frac{\phi(\Omega_\epsilon)-\phi(\Omega)} {\pi\epsilon^2} \tag{19} $$$$ \Omega_\tau= \{p_\tau\in\mathbb R^2\mid p_\tau=p+\tau n,\ p\in\Omega_\epsilon\} \tag{20} $$$$ T(p)= \frac4{1+\nu}\sigma:\epsilon - \frac{1-3\nu}{1-\nu^2} tr(\sigma)tr(\epsilon). \tag{21} $$Sehemu ya modified HJE inaandika forcing term $g=-sign(\psi)T$, lakini sentensi hiyo pia inataja positive weight factor $w$. $w$ haipo kwenye formula iliyoonyeshwa, hivyo tofauti hiyo ya chanzo haijasahihishwa kimya kimya.ESO, BESO na PareTO$$ \Omega_\tau=\{p\mid D\phi(p)>\tau\} \tag{22} $$$$ \Omega_{\tau^-}^{keep} =\{p\in\Omega\mid\alpha(p)>\tau^-\} \tag{23} $$$$ \Omega_{\tau^+}^{add} =\{p\in\Omega\mid\alpha(p)>\tau^+\} \tag{24} $$$$ \begin{aligned} \min_{\Omega(x)\subseteq D}\;&\{V,\phi(d)\}\ V(x)&\le V^*,\ R_{el}(d)&=0. \end{aligned} \tag{25} $$$$ \Delta V(\Omega_1,\Omega_2) = V(\Omega_1\setminus\Omega_2) + V(\Omega_2\setminus\Omega_1) \le\delta. \tag{26} $$ESO huondoa material bila kuirudisha. BESO inaruhusu removal na re-introduction. PareTO inalenga local Pareto optimality kwa volume levels zinazofuatana na hutumia fixed-point iteration katika kila outer step.Minimum feature size na physical-density projection$$ \chi_e= \begin{cases} 1,&e\in\Omega_{design}\ 0,&\text{vinginevyo} \end{cases} \tag{27} $$$$ \tilde\rho_e= \frac{\sum_iH_{ei}\chi_i\rho_i} {\sum_iH_{ei}\chi_i} \tag{28} $$$$ H_{ei}= \begin{cases} r_{\min}-dist(e,i),&dist(e,i)\le r_{\min}\ 0,&\text{vinginevyo} \end{cases} \tag{29} $$$$ \frac{\partial\phi}{\partial\rho_i} = \sum_e \frac{\partial\phi}{\partial\tilde\rho_e} \frac{\partial\tilde\rho_e}{\partial\rho_i} \tag{30} $$$$ \frac{\partial\tilde\rho_e}{\partial\rho_i} = \frac{H_{ei}\chi_i}{\sum_jH_{ej}\chi_j} \tag{31} $$$$ \widehat{\left(\frac{\partial\phi}{\partial\rho_i}\right)} = \frac1{\max(\rho_i,\epsilon)} \sum_eH_{ei}\rho_i \frac{\partial\phi}{\partial\tilde\rho_e}, \quad\epsilon=10^{-3} \tag{32} $$$$ \hat\rho_e= \frac{\tanh(\beta\eta)+\tanh[\beta(\rho_e-\eta)]} {\tanh(\beta\eta)+\tanh[\beta(1-\eta)]} \tag{33} $$$$ \frac{\partial\hat\rho_e}{\partial\rho_e} = \frac{\beta[1-\tanh^2(\beta(\rho_e-\eta))]} {\tanh(\beta\eta)+\tanh[\beta(1-\eta)]} \tag{34} $$$$ \frac{\partial\phi}{\partial\rho_e} = \frac{\partial\phi}{\partial\hat\rho_e} \frac{\partial\hat\rho_e}{\partial\rho_e} \tag{35} $$$$ \frac{\partial\phi}{\partial\rho_i} = \sum_e \frac{\partial\phi}{\partial\hat\rho_e} \frac{\partial\hat\rho_e}{\partial\tilde\rho_e} \frac{\partial\tilde\rho_e}{\partial\rho_i}. \tag{36} $$Filter ya minimum feature size hupunguza checkerboard na thin members. Heaviside projection huongeza ukali wa mabadiliko ya material; katika chanzo $\eta=0.5$ na mifano ya $\beta=1,8,64$ inaonyeshwa.Retained regions$$ \rho_e^{filtered}=1 \quad\text{ikiwa}\quad\chi_e^{ret}=1 \tag{37} $$$$ \left.\frac{\partial\phi}{\partial\rho_e}\right|_{\chi_e^{ret}=1} = \min_i\left(\frac{\partial\phi}{\partial\rho_i}\right) \tag{38} $$$$ \left.\frac{\partial\phi}{\partial\phi_e}\right|_{\chi_e^{ret}=1}=0 \tag{39} $$$$ \left.\frac{\partial\phi}{\partial\rho_e}\right|_{\chi_e^{ret}=1} = \max_i\left(\frac{\partial\phi}{\partial\rho_i}\right). \tag{40} $$Gripper yenye elementi 10,000, PETG $E=2$ GPa, $\nu=0.35$, force 10 N na volume fraction 0.65: bila retain $C/C_0=0.32$; kwa circular regions retained $C/C_0=0.33$.Multiple loads, self-weight na heat conduction$$ C_{avg} = \frac1{N_L} \sum_{\ell=1}^{N_L}F^{(\ell)T}d^{(\ell)} \tag{41} $$Cantilever yenye elementi 3,200, $E=100$ GPa, $\nu=0.3$, volume fraction 0.5; loads ni $F_1=+200$ kN na $F_2=-100$ kN. Average compliance: LSSO 2.11, standard HJE 1.84, modified HJE 1.68, SIMP 1.89, PareTO 1.70 N·m.$$ \begin{aligned} \min_\rho\;&\phi(d;\rho) \tag{42a}\ \sum_e\rho_ev_e-V^*&\le0 \tag{42b}\ K_{el}(\rho)d-f_{el}-b(\rho)&=0 \tag{42c}\ 0<\rho_{\min}\le\rho_e&\le1. \tag{42d} \end{aligned} $$$$ \rho_e^{eff}=\rho_e\rho_e^{mat} \tag{43} $$$$ b=\sum_e\rho_e^{eff}a_ev_e \tag{44} $$$$ b'=\rho_e^{mat}a_ev_e. \tag{45} $$Bridge self-weight: elementi 3,000, $E=100$ GPa, $\nu=0.3$, density ya material 1000 kg/m³, $g=[0,-10]$ m/s².$$ \begin{aligned} \nabla\cdot(\kappa\nabla T)+f&=0 \tag{46a}\ T-T_0&=0 \tag{46b}\ (\kappa\nabla T)\cdot n-q_n(x)&=0. \tag{46c} \end{aligned} $$$$ \begin{aligned} \min_\rho\;&T^\top K_{th}(\rho)T \tag{47a}\ \sum_e\rho_ev_e-V^*&\le0 \tag{47b}\ K_{th}(\rho)T-f_{th}&=0 \tag{47c}\ 0<\rho_{\min}\le\rho_e&\le1. \tag{47d} \end{aligned} $$Mifano ya joto hutumia elementi 10,000 na volume fraction 0.5. Boundary heat flux: $\kappa=1$, $q_n=1$ W/m², $T=0$ K, $f=0$, SIMP p=3, OC. Internal heat generation: $f=0.01$ W/m³, RAMP q=5, OC.Stress minimization, local volume na fluid$$ \tilde\sigma_{vm,e} = \rho_e^{q_{vm}}\sigma_{vm,e} \tag{48} $$$$ \sigma_{PN} = \left( \sum_e\tilde\sigma_{vm,e}^{p_{vm}} \right)^{1/p_{vm}} \tag{49} $$$$ \begin{aligned} \min_\rho\;&\sigma_{PN}(d;\rho) \tag{50a}\ \sum_e\rho_ev_e-V^*&\le0 \tag{50b}\ R_{el}(d;\rho)&=0 \tag{50c}\ 0<\rho_{\min}\le\rho_e&\le1. \tag{50d} \end{aligned} $$$$ \frac{d\sigma_{PN}}{d\rho_e} = \frac{\partial\sigma_{PN}}{\partial\hat\rho_e} \frac{\partial\hat\rho_e}{\partial\bar\rho_e} \frac{\partial\bar\rho_e}{\partial\rho_e} \tag{51} $$$$ \frac{d\sigma_{PN}}{d\rho} = \frac{\partial\sigma_{PN}}{\partial\rho} + \lambda^\top\frac{\partial F}{\partial\rho} \tag{52} $$$$ K(\rho)^\top\lambda= \frac{\partial\sigma_{PN}}{\partial d}. \tag{53} $$Stress example: elementi 6,000, SIMP p=3, $E=100$ GPa, $\nu=0.3$, $p_{vm}=6$; peak von Mises inapungua kutoka 60.6 MPa hadi 23.0 MPa.Local-volume beam ina elementi 80,000, local fraction 0.5 na radius 6. Prose ya chanzo inasema p-norm p=6 lakini code ina localPNorm=16. Gripper local-volume ina elementi 80,000 active, local fraction 0.65, radius 10 na prose p=6.Fluid wrapper: steady laminar incompressible Navier–Stokes + Brinkman. Pipe bend/double pipe hutumia elementi 2,000, SIMP p=3, MMA, $V_f=0.3$, $U_{in}=1$ m/s, $\rho=1$ kg/m³, $\mu=1$ kg/(m·s). Wind tunnel hutumia elementi 40,000, Re=10, active design rectangle yenye center [1.35,0.5] m, width 1.5 m na height 0.5 m. Objectives ni energy dissipation, drag minimization na lift maximization.Umuhimu unaowezekana katika Afrika MasharikiUtafiti haujafanywa kwa data ya Afrika Mashariki na hauonyeshi kuwa designs hizi zimehakikiwa moja kwa moja katika viwanda au vyuo vya eneo hilo. Hata hivyo framework huria ya MATLAB inaweza kuwa muhimu kwa elimu ya computational mechanics, mechanical/aerospace engineering, additive manufacturing na thermal-fluid design katika eneo hilo. Matumizi ya ndani yatahitaji kuthibitisha material properties, manufacturing tolerances, upatikanaji wa MATLAB, uwezo wa computation na experimental validation kulingana na mazingira ya taasisi au sekta husika.Utafiti unasema nini na hauseni nini?

Accepted Answer

Unaonyesha kwamba familia nyingi za SO/TO zinaweza kuunganishwa katika architecture moja ya programu na kwamba new functionals/constraints zinaweza kuongezwa bila kuandika upya core optimizer. Hauseti kuwa STORX ni fastest solver, kwamba PareTO ni bora kwa kila tatizo, kwamba designs ni global optima, au kwamba benchmark za 2D ni uthibitisho wa moja kwa moja wa industrial-scale performance.

Mbinu / mfano	C (N·m)	δmax (m)	σvm,max (MPa)
LSSO Cantilever bottom	7.85	9.37e-05	10.5
LSSO Cantilever middle	12.5	9.99e-05	4.93
LSSO L-bracket top	25.8	2.76e-04	37.8
LSSO L-bracket mid	25.7	2.89e-04	54.3
LSSO MBB	22.7	2.48e-04	6.18
SIMP-OC Cantilever bottom	6.98	7.46e-05	6.94
SIMP-OC Cantilever middle	10.6	8.50e-05	8.83
SIMP-OC L-bracket top	22.9	2.46e-04	21.0
SIMP-OC L-bracket mid	21.7	2.42e-04	23.0
SIMP-OC MBB	15.0	1.64e-04	6.98
Standard HJE Cantilever bottom	6.38	6.85e-05	2.34
Standard HJE Cantilever middle	9.68	7.84e-05	2.83
Standard HJE L-bracket top	21.2	2.27e-04	25.2
Standard HJE L-bracket mid	19.7	2.21e-04	36.1
Standard HJE MBB	14.0	1.53e-04	3.98
Modified HJE Cantilever bottom	6.31	6.70e-05	2.59
Modified HJE Cantilever middle	9.65	7.76e-05	3.06
Modified HJE L-bracket top	20.1	2.20e-04	9.49
Modified HJE L-bracket mid	19.3	2.19e-04	29.5
Modified HJE MBB	13.7	1.50e-04	4.74

Mfano / mbinu	C (N·m)	δmax (m)	σvm,max (MPa)	Source
Cantilever bottom — ESO	6.48	6.89e-05	4.52	Table 6
Cantilever bottom — BESO	6.43	6.86e-05	5.79	Table 6
Cantilever bottom — PareTO	6.32	6.74e-05	3.24	Table 6
Cantilever middle — ESO	9.76	7.83e-05	6.69	Table 6
Cantilever middle — BESO	9.76	7.83e-05	6.69	Table 6
Cantilever middle — PareTO	9.59	7.69e-05	3.28	Table 6
L-bracket top — ESO	20.4	2.23e-04	7.99	Table 6
L-bracket top — BESO	20.4	2.23e-04	7.99	Table 6
L-bracket top — PareTO	20.3	2.21e-04	8.01	Table 6
L-bracket mid — ESO	21.2	3.20e-04	490	Table 6
L-bracket mid — BESO	21.2	3.20e-04	490	Table 6
L-bracket mid — PareTO	19.2	2.16e-04	19.6	Table 6
MBB — ESO	14.2	1.55e-04	19.4	Table 6
MBB — BESO	14.2	1.55e-04	19.4	Table 6
MBB — PareTO	13.4	1.46e-04	5.39	Table 6

STORX: Mfumo huria wa MATLAB unaounganisha uboreshaji wa umbo na topolojia kwa usanifu unaolenga vitu

Tatizo linalolengwa

Usanifu wa object-oriented

B-Rep na FEA

Parametric shape optimization

Level-set shape optimization

Density-based topology optimization

Level-set TO na topological sensitivity

ESO, BESO na PareTO

Minimum feature size na physical-density projection

Retained regions

Multiple loads, self-weight na heat conduction

Stress minimization, local volume na fluid

Umuhimu unaowezekana katika Afrika Mashariki

Utafiti unasema nini na hauseni nini?

Mbinu na Matokeo ya Utafiti

Verianla Live: ESO, BESO na PareTO

Maelezo ya Chanzo na Mbinu

Acha maoni

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