{"id":20101,"date":"2026-11-01T07:12:53","date_gmt":"2026-11-01T07:12:53","guid":{"rendered":"https:\/\/ccitonline.com\/wp\/?p=20101"},"modified":"2026-11-01T07:12:53","modified_gmt":"2026-11-01T07:12:53","slug":"landasan-matematis-analisis-struktur-menara-turbin-angin-dengan-metode-fem-autodesk-inventor-project-komputasi-teknik-ganang-adhitama-2606829613","status":"publish","type":"post","link":"https:\/\/ccitonline.com\/wp\/2026\/11\/01\/landasan-matematis-analisis-struktur-menara-turbin-angin-dengan-metode-fem-autodesk-inventor-project-komputasi-teknik-ganang-adhitama-2606829613\/","title":{"rendered":"Landasan Matematis Analisis Struktur Menara Turbin Angin dengan Metode FEM Autodesk Inventor &#8211; Project Komputasi Teknik &#8211; Ganang Adhitama (2606829613)"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"1024\" src=\"https:\/\/ccitonline.com\/wp\/wp-content\/uploads\/2026\/11\/WhatsApp-Image-2026-11-01-at-13.56.29-768x1024-1.jpeg\" alt=\"\" class=\"wp-image-20107\" srcset=\"https:\/\/ccitonline.com\/wp\/wp-content\/uploads\/2026\/11\/WhatsApp-Image-2026-11-01-at-13.56.29-768x1024-1.jpeg 768w, https:\/\/ccitonline.com\/wp\/wp-content\/uploads\/2026\/11\/WhatsApp-Image-2026-11-01-at-13.56.29-225x300.jpeg 225w, https:\/\/ccitonline.com\/wp\/wp-content\/uploads\/2026\/11\/WhatsApp-Image-2026-11-01-at-13.56.29-1152x1536.jpeg 1152w, https:\/\/ccitonline.com\/wp\/wp-content\/uploads\/2026\/11\/WhatsApp-Image-2026-11-01-at-13.56.29.jpeg 1200w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<style>\n#fem-notes-26 {\n  width: 100%;\n  max-width: 980px;\n  margin: 0 auto;\n  padding: 24px;\n  box-sizing: border-box;\n  position: static;\n  transform: none;\n  background: #ffffff;\n  color: #263747;\n  font-family: Arial, Helvetica, sans-serif;\n  font-size: 15px;\n  line-height: 1.8;\n}\n\n#fem-notes-26 * {\n  box-sizing: border-box;\n}\n\n#fem-notes-26 p {\n  margin: 0 0 15px;\n}\n\n#fem-notes-26 h2 {\n  font-size: 20px;\n  line-height: 1.4;\n  font-weight: 700;\n  color: #135b81;\n  margin: 30px 0 12px;\n  padding-bottom: 8px;\n  border-bottom: 1px solid #dce7ec;\n}\n\n#fem-notes-26 .opening {\n  margin-bottom: 22px;\n}\n\n#fem-notes-26 .formula {\n  margin: 15px 0;\n  padding: 14px 12px;\n  background: #f6f9fb;\n  border: 1px solid #e2eaf0;\n  border-radius: 9px;\n  text-align: center;\n  overflow-x: auto;\n}\n\n#fem-notes-26 .math {\n  font-family: Georgia, \"Times New Roman\", serif;\n  font-size: 21px;\n  line-height: 1.7;\n  color: #174d71;\n  white-space: nowrap;\n}\n\n#fem-notes-26 .math.small {\n  font-size: 17px;\n}\n\n#fem-notes-26 .formula.primary {\n  border-color: #a8d3d6;\n  background: #f3fbfa;\n}\n\n#fem-notes-26 .eq-name {\n  font: 11px Arial, sans-serif;\n  color: #6a7d88;\n  letter-spacing: .4px;\n  margin-bottom: 5px;\n}\n\n#fem-notes-26 .notation {\n  font-size: 13px;\n  color: #596a76;\n  margin: 8px 0 18px;\n}\n\n#fem-notes-26 .fig {\n  margin: 20px 0;\n  padding: 18px;\n  border: 1px solid #e0e9ee;\n  border-radius: 12px;\n  background: #ffffff;\n}\n\n#fem-notes-26 .fig-title {\n  text-align: center;\n  font-weight: 700;\n  color: #365369;\n  font-size: 14px;\n  margin-bottom: 12px;\n}\n\n#fem-notes-26 svg {\n  width: 100%;\n  height: auto;\n  display: block;\n}\n\n#fem-notes-26 .fig-caption {\n  font-size: 12px;\n  color: #657582;\n  text-align: center;\n  margin: 8px 0 0;\n}\n\n#fem-notes-26 .load-controls {\n  display: flex;\n  gap: 10px;\n  flex-wrap: wrap;\n  justify-content: center;\n  margin-bottom: 12px;\n}\n\n#fem-notes-26 .load-controls label {\n  display: inline-flex;\n  align-items: center;\n  gap: 7px;\n  padding: 6px 11px;\n  background: #fff;\n  border: 1px solid #dfe8ec;\n  border-radius: 7px;\n  font-size: 12px;\n  cursor: pointer;\n  color: #425665;\n}\n\n#fem-notes-26 .load-controls input {\n  accent-color: #15848a;\n  cursor: pointer;\n}\n\n#fem-notes-26 .flow {\n  display: flex;\n  flex-wrap: wrap;\n  justify-content: center;\n  align-items: center;\n  gap: 8px;\n  margin: 18px 0;\n}\n\n#fem-notes-26 .flow-step {\n  border: 1px solid #dce6ed;\n  background: #f7fafb;\n  border-radius: 8px;\n  padding: 9px 13px;\n  font-size: 12px;\n  text-align: center;\n  font-weight: 600;\n  color: #244e69;\n}\n\n#fem-notes-26 .flow-step.last {\n  border-color: #93cac5;\n  background: #edf9f6;\n  color: #12665f;\n}\n\n#fem-notes-26 .flow-arrow {\n  color: #15848a;\n  font-size: 19px;\n}\n\n#fem-notes-26 .closing {\n  margin-top: 26px;\n  padding-top: 14px;\n  border-top: 1px solid #e0e9ed;\n}\n\n@media(max-width:600px) {\n  #fem-notes-26 {\n    padding: 14px 8px;\n    font-size: 14px;\n  }\n\n  #fem-notes-26 h2 {\n    font-size: 18px;\n  }\n\n  #fem-notes-26 .math {\n    font-size: 18px;\n  }\n\n  #fem-notes-26 .math.small {\n    font-size: 15px;\n  }\n\n  #fem-notes-26 .fig {\n    padding: 9px;\n  }\n\n  #fem-notes-26 .load-controls {\n    gap: 5px;\n  }\n\n  #fem-notes-26 .load-controls label {\n    font-size: 11px;\n    padding: 5px 7px;\n  }\n}\n<\/style>\n\n<article id=\"fem-notes-26\">\n\n  <div class=\"opening\">\n\n    <p>\n      Assalamualaikum warahmatullahi wabarakatuh.\n    <\/p>\n\n    <p>\n      <strong>Bismillahirrahmanirrahim.<\/strong>\n    <\/p>\n\n    <p>\n      Pada proyek Komputasi Teknik ini, saya melakukan\n      analisis struktur menara turbin angin menggunakan\n      metode <em>Finite Element Method<\/em> (FEM)\n      melalui Autodesk Inventor Professional 2024.\n      Analisis dilakukan dengan pendekatan\n      <em>3D Linear Static Analysis<\/em>\n      untuk menghitung perpindahan (displacement)\n      struktur akibat rotor thrust, wind drag,\n      dan gaya gravitasi.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ======================================= -->\n  <!-- REVISED WIND TURBINE ILLUSTRATION       -->\n  <!-- ======================================= -->\n\n  <div class=\"fig\">\n\n    <div class=\"fig-title\">\n      Ilustrasi Model dan Pembebanan Menara Turbin Angin\n    <\/div>\n\n    <div class=\"load-controls\">\n\n      <label>\n        <input type=\"checkbox\" data-toggle=\"thrust\" checked=\"\">\n        Rotor thrust\n      <\/label>\n\n      <label>\n        <input type=\"checkbox\" data-toggle=\"drag\" checked=\"\">\n        Wind drag\n      <\/label>\n\n      <label>\n        <input type=\"checkbox\" data-toggle=\"weight\" checked=\"\">\n        Weight\n      <\/label>\n\n    <\/div>\n\n\n    <svg viewBox=\"0 0 720 435\" role=\"img\" aria-label=\"Vertical cantilever wind turbine tower, with rotor thrust, wind drag, gravity and conceptual bending displacement\">\n\n      <defs>\n\n        <marker id=\"fem26-blue\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"6\" markerHeight=\"6\" orient=\"auto\">\n\n          <path d=\"M0 0 L10 5 L0 10 Z\" fill=\"#1687bd\"><\/path>\n\n        <\/marker>\n\n        <marker id=\"fem26-orange\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"6\" markerHeight=\"6\" orient=\"auto\">\n\n          <path d=\"M0 0 L10 5 L0 10 Z\" fill=\"#dc8733\"><\/path>\n\n        <\/marker>\n\n        <marker id=\"fem26-green\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"6\" markerHeight=\"6\" orient=\"auto\">\n\n          <path d=\"M0 0 L10 5 L0 10 Z\" fill=\"#159486\"><\/path>\n\n        <\/marker>\n\n      <\/defs>\n\n\n      <!-- =================================== -->\n      <!-- DEFORMED TOWER: CANTILEVER BENDING -->\n      <!-- =================================== -->\n\n      <!--\n        The bottom remains fixed.\n\n        Lateral displacement increases\n        progressively toward the top.\n\n        The curved shape represents\n        exaggerated elastic bending.\n\n        It is not actual simulation data.\n      -->\n\n      <g id=\"fem26-deformed-tower\">\n\n        <!-- Deformed tower silhouette -->\n\n        <path d=\"\n            M394 132\n            C368 166 348 214 325 273\n            C302 323 292 358 289 374\n            L390 374\n            C390 329 393 272 397 237\n            C406 190 416 154 416 132\n            Z\n          \" fill=\"#20a99c\" fill-opacity=\"0.10\" stroke=\"#159486\" stroke-width=\"2.3\" stroke-dasharray=\"7 5\" stroke-linejoin=\"round\"><\/path>\n\n        <!-- Curved centerline -->\n\n        <path d=\"\n            M339 374\n            C340 311 366 208 405 132\n         \n        &lt;!-- Top displacement indicator --&gt;\n\n        \n\n\n        &lt;path d=\" m460=\"\" 247=\"\" l414=\"\" 247\"=\"\" stroke=\"#159486\" stroke-width=\"1.3\" fill=\"none\" stroke-dasharray=\"3 4\"><\/path>\n\n      <\/g>\n\n\n      <!-- =================================== -->\n      <!-- ORIGINAL UNDEFORMED TOWER          -->\n      <!-- =================================== -->\n\n      <g id=\"fem26-original-tower\">\n\n        <path d=\"\n            M329 132\n            L351 132\n            L390 374\n            L289 374\n            Z\n          \" fill=\"#e5ebf0\" stroke=\"#536b7d\" stroke-width=\"2.3\" stroke-linejoin=\"round\"><\/path>\n\n        <!-- Vertical reference centerline -->\n\n        <line x1=\"340\" y1=\"132\" x2=\"340\" y2=\"374\" stroke=\"#9aabb5\" stroke-width=\"1.3\" stroke-dasharray=\"5 5\"><\/line>\n\n      <\/g>\n\n\n      <!-- =================================== -->\n      <!-- TURBINE AND ROTOR                   -->\n      <!-- =================================== -->\n\n      <g id=\"fem26-rotor\">\n\n        <!-- Nacelle -->\n\n        <rect x=\"335\" y=\"109\" width=\"49\" height=\"21\" rx=\"5\" fill=\"#668092\"><\/rect>\n\n        <!-- Hub -->\n\n        <circle cx=\"334\" cy=\"119\" r=\"7\" fill=\"#436477\"><\/circle>\n\n        <!-- Rotor blades -->\n\n        <g stroke=\"#688394\" stroke-width=\"5.8\" stroke-linecap=\"round\" fill=\"none\">\n\n          <path d=\"M334 119 L319 61\"><\/path>\n\n          <path d=\"M334 119 L297 156\"><\/path>\n\n          <path d=\"M334 119 L378 146\"><\/path>\n\n        <\/g>\n\n        <circle cx=\"334\" cy=\"119\" r=\"4\" fill=\"#355669\"><\/circle>\n\n      <\/g>\n\n\n      <!-- =================================== -->\n      <!-- ROTOR THRUST: LEFT OF TURBINE      -->\n      <!-- =================================== -->\n\n      <g data-force=\"thrust\">\n\n        <path d=\"M157 105 L292 105\" stroke=\"#dc8733\" stroke-width=\"3\" fill=\"none\" marker-end=\"url(#fem26-orange)\"><\/path>\n\n        <text x=\"222\" y=\"87\" font-size=\"14\" fill=\"#cf7c26\" text-anchor=\"middle\">\n          Rotor thrust\n        <\/text>\n\n      <\/g>\n\n\n      <!-- =================================== -->\n      <!-- WIND DRAG: LEFT OF TOWER           -->\n      <!-- =================================== -->\n\n      <g data-force=\"drag\">\n\n        <!--\n          Top arrow is longest.\n          Bottom arrow is shortest.\n\n          All arrow tips stop before\n          reaching the tower.\n        -->\n\n        <g stroke=\"#1687bd\" stroke-width=\"2.8\" fill=\"none\" marker-end=\"url(#fem26-blue)\">\n\n          <path d=\"M140 195 L277 195\"><\/path>\n\n          <path d=\"M166 239 L277 239\"><\/path>\n\n          <path d=\"M190 283 L277 283\"><\/path>\n\n          <path d=\"M211 327 L277 327\"><\/path>\n\n        <\/g>\n\n        <text x=\"93\" y=\"253\" text-anchor=\"middle\" font-size=\"14\" fill=\"#1687bd\">\n          Wind drag\n        <\/text>\n\n      <\/g>\n\n\n      <!-- =================================== -->\n      <!-- GRAVITY: UNDER THE TURBINE         -->\n      <!-- =================================== -->\n\n      <g data-force=\"weight\">\n\n        <!-- Vertical downward arrow -->\n\n        <path d=\"M342 141 L342 177\" stroke=\"#dc8733\" stroke-width=\"2.8\" fill=\"none\" marker-end=\"url(#fem26-orange)\"><\/path>\n\n        <text x=\"320\" y=\"197\" font-size=\"12.5\" fill=\"#cf7c26\">\n          Weight\n        <\/text>\n\n      <\/g>\n\n\n      <!-- =================================== -->\n      <!-- FIXED FOUNDATION                   -->\n      <!-- =================================== -->\n\n      <g id=\"fem26-foundation\">\n\n        <rect x=\"273\" y=\"375\" width=\"135\" height=\"13\" fill=\"#647b8b\"><\/rect>\n\n        <g stroke=\"#758a98\" stroke-width=\"1.5\" fill=\"none\">\n\n          <path d=\"M284 388 L272 402\"><\/path>\n          <path d=\"M304 388 L292 402\"><\/path>\n          <path d=\"M324 388 L312 402\"><\/path>\n          <path d=\"M344 388 L332 402\"><\/path>\n          <path d=\"M364 388 L352 402\"><\/path>\n          <path d=\"M384 388 L372 402\"><\/path>\n          <path d=\"M404 388 L392 402\"><\/path>\n\n        <\/g>\n\n        <text x=\"340\" y=\"421\" text-anchor=\"middle\" font-size=\"13\" fill=\"#536b7d\">\n          Fixed support\n        <\/text>\n\n      <\/g>\n\n    <\/svg>\n\n\n    <p class=\"fig-caption\">\n      Ilustrasi konseptual pembebanan dan deformasi menara\n      cantilever. Bentuk awal ditampilkan berwarna abu-abu,\n      sedangkan bentuk setelah deformasi ditunjukkan\n      oleh garis lengkung hijau. Displacement bernilai\n      nol pada fixed support dan meningkat menuju\n      bagian atas menara. Bentuk deformasi diperbesar\n      untuk keperluan ilustrasi.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ======================================= -->\n  <!-- SECTION 1                               -->\n  <!-- ======================================= -->\n\n  <h2>\n    1. Landasan Matematis:\n    Hukum Newton hingga Navier\u2013Cauchy\n  <\/h2>\n\n  <p>\n    Dasar analisis struktur berasal dari Hukum II Newton,\n    yang dalam kondisi statis memiliki percepatan nol.\n    Oleh karena itu, resultan gaya pada struktur\n    harus berada dalam kesetimbangan.\n  <\/p>\n\n  <div class=\"formula\">\n\n    <div class=\"math\">\n      \u03a3F = ma &nbsp; \u2192 &nbsp; \u03a3F = 0\n    <\/div>\n\n  <\/div>\n\n  <p>\n    Dalam mekanika kontinum, prinsip tersebut diterapkan\n    pada setiap elemen volume material sehingga\n    menghasilkan persamaan kesetimbangan elastisitas:\n  <\/p>\n\n  <div class=\"formula\">\n\n    <div class=\"math\">\n      \u2207 \u00b7 \u03c3 + b = 0\n    <\/div>\n\n  <\/div>\n\n  <p>\n    Untuk menghubungkan gaya dengan perpindahan,\n    digunakan persamaan regangan\u2013perpindahan\n    serta Hukum Hooke dalam notasi matriks:\n  <\/p>\n\n  <div class=\"formula\">\n\n    <div class=\"math\">\n      \u03b5 = \u00bd [\u2207u + (\u2207u)<sup>T<\/sup>]\n    <\/div>\n\n    <div class=\"math\">\n      \u03c3 = D\u03b5\n    <\/div>\n\n  <\/div>\n\n  <p>\n    Substitusi hubungan tersebut ke dalam persamaan\n    kesetimbangan, dengan asumsi material homogen,\n    isotropik, dan elastis linear, menghasilkan\n    <strong>persamaan Navier\u2013Cauchy<\/strong>:\n  <\/p>\n\n  <div class=\"formula primary\">\n\n    <div class=\"eq-name\">\n      GOVERNING EQUATION \u2014 PDE ORDE DUA\n    <\/div>\n\n    <div class=\"math small\">\n      \u03bc\u2207\u00b2u + (\u03bb + \u03bc)\u2207(\u2207 \u00b7 u) + b = 0\n    <\/div>\n\n  <\/div>\n\n  <p class=\"notation\">\n    Keterangan:\n    \u03c3 = tensor tegangan (Pa);\n    b = gaya per satuan volume (N\/m\u00b3);\n    u = vektor displacement (m);\n    \u03b5 = regangan (tanpa satuan);\n    D = matriks elastisitas (Pa);\n    \u03bb dan \u03bc = konstanta Lam\u00e9 (Pa);\n    \u2207\u00b2 = operator Laplacian.\n  <\/p>\n\n\n  <!-- ======================================= -->\n  <!-- SECTION 2                               -->\n  <!-- ======================================= -->\n\n  <h2>\n    2. Transformasi Persamaan ke Weak Formulation\n  <\/h2>\n\n  <p>\n    Persamaan Navier\u2013Cauchy merupakan persamaan\n    diferensial parsial dalam bentuk kontinu\n    (<em>strong form<\/em>). FEM mengubah persamaan\n    kesetimbangan yang ekuivalen menjadi\n    <em>weak formulation<\/em> dengan mengalikannya\n    dengan perpindahan virtual dan mengintegrasikan\n    terhadap volume struktur.\n  <\/p>\n\n  <div class=\"formula\">\n\n    <div class=\"math small\">\n      \u222b<sub>\u03a9<\/sub> \u03b4u<sup>T<\/sup>\n      (\u2207 \u00b7 \u03c3 + b) dV = 0\n    <\/div>\n\n  <\/div>\n\n  <p>\n    Melalui integrasi parsial dan Teorema Divergensi,\n    diperoleh prinsip kerja virtual, yaitu kesetimbangan\n    kerja internal dan eksternal:\n  <\/p>\n\n  <div class=\"formula primary\">\n\n    <div class=\"eq-name\">\n      WEAK FORMULATION\n    <\/div>\n\n    <div class=\"math small\">\n      \u222b<sub>\u03a9<\/sub> \u03b4\u03b5<sup>T<\/sup>\u03c3 dV\n    <\/div>\n\n    <div class=\"math small\">\n      =\n    <\/div>\n\n    <div class=\"math small\">\n      \u222b<sub>\u03a9<\/sub> \u03b4u<sup>T<\/sup>b dV\n      + \u222b<sub>\u0393t<\/sub> \u03b4u<sup>T<\/sup>t dA\n    <\/div>\n\n  <\/div>\n\n  <p class=\"notation\">\n    \u03b4u = perpindahan virtual (m);\n    \u03b4\u03b5 = regangan virtual (tanpa satuan);\n    \u03a9 = domain volume struktur;\n    \u0393t = permukaan yang menerima gaya;\n    t = gaya permukaan per satuan luas (Pa).\n    Beban titik dapat ditambahkan sebagai kerja virtual\n    eksternal apabila digunakan dalam model.\n  <\/p>\n\n\n  <!-- ======================================= -->\n  <!-- SECTION 3                               -->\n  <!-- ======================================= -->\n\n  <h2>\n    3. Diskretisasi FEM dan Matriks Kekakuan\n  <\/h2>\n\n  <p>\n    Selanjutnya, geometri menara dibagi menjadi\n    elemen-elemen kecil melalui <em>meshing<\/em>.\n    Displacement di dalam setiap elemen diaproksimasi\n    menggunakan <em>shape functions<\/em>:\n  <\/p>\n\n  <div class=\"formula\">\n\n    <div class=\"math\">\n      u<sup>(e)<\/sup> = N d<sup>(e)<\/sup>\n    <\/div>\n\n    <div class=\"math\">\n      \u03b5<sup>(e)<\/sup> = B d<sup>(e)<\/sup>\n    <\/div>\n\n    <div class=\"math\">\n      \u03c3<sup>(e)<\/sup> = D B d<sup>(e)<\/sup>\n    <\/div>\n\n  <\/div>\n\n  <p>\n    Dengan mensubstitusikan hubungan tersebut ke dalam\n    weak formulation dan menggunakan pendekatan Galerkin,\n    diperoleh persamaan keseimbangan elemen:\n  <\/p>\n\n  <div class=\"formula\">\n\n    <div class=\"math small\">\n      [ \u222b<sub>\u03a9e<\/sub> B<sup>T<\/sup> D B dV ]\n      d<sup>(e)<\/sup> = f<sup>(e)<\/sup>\n    <\/div>\n\n  <\/div>\n\n  <p>\n    Bagian di dalam kurung merupakan\n    <strong>matriks kekakuan elemen<\/strong>:\n  <\/p>\n\n  <div class=\"formula primary\">\n\n    <div class=\"eq-name\">\n      ELEMENT STIFFNESS MATRIX\n    <\/div>\n\n    <div class=\"math\">\n      K<sup>(e)<\/sup> =\n      \u222b<sub>\u03a9e<\/sub> B<sup>T<\/sup> D B dV\n    <\/div>\n\n  <\/div>\n\n  <p class=\"notation\">\n    N = matriks shape functions (tanpa satuan);\n    d<sup>(e)<\/sup> = displacement nodal elemen (m);\n    B = matriks strain\u2013displacement (1\/m);\n    D = matriks elastisitas (Pa);\n    K<sup>(e)<\/sup> = matriks kekakuan elemen (N\/m);\n    f<sup>(e)<\/sup> = gaya nodal ekuivalen (N).\n  <\/p>\n\n\n  <!-- ======================================= -->\n  <!-- SECTION 4                               -->\n  <!-- ======================================= -->\n\n  <h2>\n    4. Persamaan yang Diselesaikan Autodesk Inventor\n  <\/h2>\n\n  <p>\n    Seluruh matriks kekakuan elemen digabungkan melalui\n    proses <em>assembly<\/em> menjadi matriks global.\n    Setelah kondisi batas diterapkan, diperoleh:\n  <\/p>\n\n  <div class=\"formula primary\">\n\n    <div class=\"eq-name\">\n      GLOBAL FINITE ELEMENT EQUATION\n    <\/div>\n\n    <div class=\"math\" style=\"font-size:27px;\">\n      KU = F\n    <\/div>\n\n  <\/div>\n\n  <p>\n    K merupakan matriks kekakuan global (N\/m),\n    U adalah vektor displacement nodal (m),\n    dan F merupakan gaya nodal global (N).\n    Pada dasar menara diterapkan\n    <em>fixed support<\/em> dengan\n    u<sub>x<\/sub> = u<sub>y<\/sub> =\n    u<sub>z<\/sub> = 0.\n  <\/p>\n\n  <p>\n    <strong>\n      Persamaan KU = F inilah yang diselesaikan\n      secara numerik oleh Autodesk Inventor\n    <\/strong>\n    untuk memperoleh displacement pada seluruh node.\n    Hasil tersebut kemudian digunakan untuk menghitung\n    strain dan stress melalui:\n  <\/p>\n\n  <div class=\"formula\">\n\n    <div class=\"math\">\n      \u03b5<sup>(e)<\/sup> = B d<sup>(e)<\/sup>\n    <\/div>\n\n    <div class=\"math\">\n      \u03c3<sup>(e)<\/sup> = D \u03b5<sup>(e)<\/sup>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ======================================= -->\n  <!-- FEM WORKFLOW                            -->\n  <!-- ======================================= -->\n\n  <div class=\"fig\">\n\n    <div class=\"fig-title\">\n      Alur Matematis FEM\n    <\/div>\n\n    <div class=\"flow\">\n\n      <div class=\"flow-step\">\n        Navier\u2013Cauchy<br>\n        PDE\n      <\/div>\n\n      <span class=\"flow-arrow\">\u2192<\/span>\n\n      <div class=\"flow-step\">\n        Weak<br>\n        Form\n      <\/div>\n\n      <span class=\"flow-arrow\">\u2192<\/span>\n\n      <div class=\"flow-step\">\n        Meshing &amp;<br>\n        Shape Functions\n      <\/div>\n\n      <span class=\"flow-arrow\">\u2192<\/span>\n\n      <div class=\"flow-step\">\n        Element<br>\n        Stiffness\n      <\/div>\n\n      <span class=\"flow-arrow\">\u2192<\/span>\n\n      <div class=\"flow-step last\">\n        KU = F<br>\n        Displacement\n      <\/div>\n\n    <\/div>\n\n    <p class=\"fig-caption\">\n      Displacement merupakan variabel utama.\n      Strain dan stress dihitung melalui post-processing.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ======================================= -->\n  <!-- SECTION 5                               -->\n  <!-- ======================================= -->\n\n  <h2>\n    5. Kesimpulan\n  <\/h2>\n\n  <p>\n    Berdasarkan penurunan matematis tersebut,\n    analisis FEM pada menara turbin angin berawal\n    dari Hukum Newton dan persamaan elastisitas\n    Navier\u2013Cauchy. Persamaan diferensial tersebut\n    ditransformasikan menjadi weak formulation,\n    kemudian didiskretisasi melalui mesh dan\n    shape functions untuk membentuk matriks kekakuan.\n  <\/p>\n\n  <p>\n    Proses assembly menghasilkan sistem persamaan\n    <strong>KU = F<\/strong>, yang diselesaikan\n    Autodesk Inventor untuk memperoleh displacement\n    sebelum menghitung distribusi strain dan stress.\n  <\/p>\n\n  <p class=\"notation\">\n    <strong>Referensi:<\/strong>\n    Hibbeler (2011),\n    <em>Mechanics of Materials<\/em>;\n    IEC 61400-2:2013;\n    Autodesk Inventor 2024 Stress Analysis Documentation.\n  <\/p>\n\n\n  <!-- ======================================= -->\n  <!-- CLOSING                                 -->\n  <!-- ======================================= -->\n\n  <div class=\"closing\">\n\n    <p>\n      Demikian pembahasan singkat mengenai\n      landasan matematis analisis struktur\n      menara turbin angin menggunakan FEM.\n    <\/p>\n\n    <p>\n      Wassalamualaikum warahmatullahi wabarakatuh.\n    <\/p>\n\n  <\/div>\n\n<\/article>\n\n\n<!-- ========================================= -->\n<!-- INTERACTIVE LOAD CONTROLS                 -->\n<!-- ========================================= -->\n\n<script>\n(function () {\n\n  function initializeFemNotes() {\n\n    var root = document.getElementById('fem-notes-26');\n\n    if (!root) return;\n\n    var toggles = root.querySelectorAll('[data-toggle]');\n\n    toggles.forEach(function (checkbox) {\n\n      var kind = checkbox.getAttribute('data-toggle');\n\n      var group = root.querySelector(\n        '[data-force=\"' + kind + '\"]'\n      );\n\n      if (!group) return;\n\n      function update() {\n        group.style.display =\n          checkbox.checked ? '' : 'none';\n      }\n\n      checkbox.addEventListener('change', update);\n\n      update();\n\n    });\n\n  }\n\n  if (document.readyState === 'loading') {\n\n    document.addEventListener(\n      'DOMContentLoaded',\n      initializeFemNotes\n    );\n\n  } else {\n\n    initializeFemNotes();\n\n  }\n\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Assalamualaikum warahmatullahi wabarakatuh. Bismillahirrahmanirrahim. Pada proyek Komputasi Teknik ini, saya melakukan analisis struktur menara turbin angin menggunakan metode Finite Element Method (FEM) melalui Autodesk Inventor Professional 2024. Analisis dilakukan dengan pendekatan 3D Linear Static Analysis untuk menghitung perpindahan (displacement) struktur akibat rotor thrust, wind drag, dan gaya gravitasi. Ilustrasi Model dan Pembebanan Menara Turbin Angin [&hellip;]<\/p>\n","protected":false},"author":651,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[],"class_list":["post-20101","post","type-post","status-publish","format-standard","hentry","category-general"],"_links":{"self":[{"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/posts\/20101","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/users\/651"}],"replies":[{"embeddable":true,"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/comments?post=20101"}],"version-history":[{"count":1,"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/posts\/20101\/revisions"}],"predecessor-version":[{"id":20110,"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/posts\/20101\/revisions\/20110"}],"wp:attachment":[{"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/media?parent=20101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/categories?post=20101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccitonline.com\/wp\/wp-json\/wp\/v2\/tags?post=20101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}